Paper Citation Record · LEDGER

Characters and fusion rules of boundary W-algebras

As of 24 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 1 inbound Pith citation observation for arXiv:2509.09039.

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pith.paper-citation-record.v1
2509.09039 v1

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Source: paper_references, paper_reference_links, observed 2026-08-04T20:01:19.124310Z

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

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Source: paper_references, paper_reference_links, observed 2026-05-17T02:44:04.510184Z

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Source: arxiv_reference, observed 2026-05-17T02:48:54.471753Z

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Outbound references

Observation bc36d2cf-8506-44a1-a672-5ca97eb72f88 · outbound

This paper cites Liouville correlation functions from four-dimensional gauge theories.Letters in Mathematical Physics, 91(2):167–197, 2010.

Characters and fusion rules of boundary W-algebras Liouville correlation functions from four-dimensional gauge theories.Letters in Mathematical Physics, 91(2):167–197, 2010

Reference 1

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Observation 6ae19b12-597a-4f79-9960-c41709cae474 · outbound

This paper cites Representation theory ofW-algebras.Inventiones mathematicae, 169(2):219–320, 2007.

Characters and fusion rules of boundary W-algebras Representation theory ofW-algebras.Inventiones mathematicae, 169(2):219–320, 2007

Reference 2

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Observation c97b460c-78e0-4745-b4f2-04cfa05bd957 · outbound

This paper cites Representation theory ofW-algebras, II.Exploring new structures and natural constructions in mathematical physics, 61:51–90, 2011.

Characters and fusion rules of boundary W-algebras Representation theory ofW-algebras, II.Exploring new structures and natural constructions in mathematical physics, 61:51–90, 2011

Reference 3

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Observation 03039eb1-ebf3-48b3-9eac-7f42448b9f17 · outbound

This paper cites Associated varieties of modules over Kac-Moody algebras andC 2-cofiniteness of W-algebras.International Mathematics Research Notices, 2015(22):11605–11666, 2015.

Characters and fusion rules of boundary W-algebras Associated varieties of modules over Kac-Moody algebras andC 2-cofiniteness of W-algebras.International Mathematics Research Notices, 2015(22):11605–11666, 2015

Reference 4

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Observation 8c7a6f19-8d0d-4e0d-abca-9c63c7a2b9a3 · outbound

This paper cites Rationality of admissible affine vertex algebras in the categoryO.Duke Mathemat- ical Journal, 165(1):67–93, 2016.

Characters and fusion rules of boundary W-algebras Rationality of admissible affine vertex algebras in the categoryO.Duke Mathemat- ical Journal, 165(1):67–93, 2016

Reference 5

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Observation fcbafe3a-ad4f-403e-b7bc-8a2181708a42 · outbound

This paper cites Modularity of relatively rational vertex algebras and fusion rules of principal affineW-algebras.Communications in Mathematical Physics, 370(1):205–247, 2019.

Characters and fusion rules of boundary W-algebras Modularity of relatively rational vertex algebras and fusion rules of principal affineW-algebras.Communications in Mathematical Physics, 370(1):205–247, 2019

Reference 6

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Observation 411a9af2-e28e-4a7c-8056-e5de12a3992a · outbound

This paper cites Rationality and fusion rules of exceptionalW-algebras.

Characters and fusion rules of boundary W-algebras Rationality and fusion rules of exceptionalW-algebras

Reference 7

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Observation 82ca01fd-259a-4659-a67d-9bd87d17acd8 · outbound

This paper cites Singularities of nilpotent Slodowy slices and collapsing levels ofW-algebras.Forum of Mathematics, Sigma, 12:95, 2024.

Characters and fusion rules of boundary W-algebras Singularities of nilpotent Slodowy slices and collapsing levels ofW-algebras.Forum of Mathematics, Sigma, 12:95, 2024

Reference 8

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Observation 78f91daa-4360-4f9b-a426-92a1cd777a29 · outbound

This paper cites American Mathematical Society Providence, RI, 2001.

Characters and fusion rules of boundary W-algebras American Mathematical Society Providence, RI, 2001

Reference 9

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Observation b9986df7-61b9-4b05-82e5-a2911a5ff37c · outbound

This paper cites Infinite chiral symmetry in four dimensions.Communications in Mathematical Physics, 336(3):1359–1433, 2015.

Characters and fusion rules of boundary W-algebras Infinite chiral symmetry in four dimensions.Communications in Mathematical Physics, 336(3):1359–1433, 2015

Reference 10

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Observation be603a28-1e73-4a5e-8b0e-26ad3fe28ebf · outbound

This paper cites Quantization of Hitchin’s integrable system and Hecke eigensheaves.

Characters and fusion rules of boundary W-algebras Quantization of Hitchin’s integrable system and Hecke eigensheaves

Reference 11

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Observation 2ba44fa3-2a35-4ba0-a4e7-c404f5be4d40 · outbound

This paper cites Number 918 in Memoirs of the American Mathematical Society.

Characters and fusion rules of boundary W-algebras Number 918 in Memoirs of the American Mathematical Society

Reference 12

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Observation f95a664d-edae-4213-a66b-0daf816b123e · outbound

This paper cites Inverse Hamiltonian reduction in typeAand generalized slices in the affine Grassmannian.arXiv preprintarXiv: 2503.

Characters and fusion rules of boundary W-algebras Inverse Hamiltonian reduction in typeAand generalized slices in the affine Grassmannian.arXiv preprintarXiv: 2503

Reference 13

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Observation 3b16701c-056f-4c6f-a080-127b34c7dd86 · outbound

This paper cites Factorized combinations of Virasoro characters.Communications in Mathematical Physics, 209(1):179–205, 2000.

Characters and fusion rules of boundary W-algebras Factorized combinations of Virasoro characters.Communications in Mathematical Physics, 209(1):179–205, 2000

Reference 14

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Observation 10b03e3f-8589-4716-a411-241f595e534c · outbound

This paper cites CRC Press, 1993.

Characters and fusion rules of boundary W-algebras CRC Press, 1993

Reference 15

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Observation 3dba3f63-7c9e-462b-975d-263233bc2659 · outbound

This paper cites Remarks on Galois symmetry in rational conformal field theories.

Characters and fusion rules of boundary W-algebras Remarks on Galois symmetry in rational conformal field theories

Reference 16

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Observation 6f4ccd74-1cf6-46cd-b91f-2346079aa39f · outbound

This paper cites Congruence subgroups and rational conformal field theory.

Characters and fusion rules of boundary W-algebras Congruence subgroups and rational conformal field theory

Reference 17

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Observation 0a0e0407-bc82-427c-8432-b9beb8f33285 · outbound

This paper cites On the structure of W-algebras in typeA.Japanese Journal of Mathematics, 20(1):1–111, 2025.

Characters and fusion rules of boundary W-algebras On the structure of W-algebras in typeA.Japanese Journal of Mathematics, 20(1):1–111, 2025

Reference 18

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Observation 142ba4f9-0312-4ed8-9a63-d409489bb0c4 · outbound

This paper cites Quantum dimensions and quantum Galois theory.Trans- actions of the American Mathematical Society, 365(12):6441–6469, 2013.

Characters and fusion rules of boundary W-algebras Quantum dimensions and quantum Galois theory.Trans- actions of the American Mathematical Society, 365(12):6441–6469, 2013

Reference 19

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Observation f8c11945-fac6-4bac-90f1-77742674886e · outbound

This paper cites Rational vertex operator algebras and the effective central charge.

Characters and fusion rules of boundary W-algebras Rational vertex operator algebras and the effective central charge

Reference 20

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Observation 5015178b-ec00-4ca6-9309-f90f225f5b4a · outbound

This paper cites Classification of good gradings of simple Lie algebras.American Mathematical Society Translations: Series 2, pages 85–104, 2005.

Characters and fusion rules of boundary W-algebras Classification of good gradings of simple Lie algebras.American Mathematical Society Translations: Series 2, pages 85–104, 2005

Reference 21

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Observation dc7f979c-25b8-4b99-b204-35241c6a83ad · outbound

This paper cites American Mathematical Soc., 2015.

Characters and fusion rules of boundary W-algebras American Mathematical Soc., 2015

Reference 22

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Observation 73b390c0-2641-413f-b0ba-3ee2e6d0f6b7 · outbound

This paper cites Andrews–Gordon type identities from combinations of Virasoro characters.The Ramanujan Journal, 17(1):33–52, 2008.

Characters and fusion rules of boundary W-algebras Andrews–Gordon type identities from combinations of Virasoro characters.The Ramanujan Journal, 17(1):33–52, 2008

Reference 23

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Observation a6219aee-ebf5-41cc-97a1-15e185a6b8f0 · outbound

This paper cites Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras.International Journal of Modern Physics A, 7(supp01a):197–215, 1992.

Characters and fusion rules of boundary W-algebras Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras.International Journal of Modern Physics A, 7(supp01a):197–215, 1992

Reference 24

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Observation 545968ea-6c77-4dde-abbc-973676b5ddf2 · outbound

This paper cites Cylindric partitions,Wr-characters and the Andrews-Gordon-Bressoud identities.Journal of Physics A: Mathematical and Theoretical, 49(16):164004, 2016.

Characters and fusion rules of boundary W-algebras Cylindric partitions,Wr-characters and the Andrews-Gordon-Bressoud identities.Journal of Physics A: Mathematical and Theoretical, 49(16):164004, 2016

Reference 25

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Observation 2df77380-dcb8-43aa-bf05-bbc8a84903d5 · outbound

This paper cites Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction.Communications in mathematical physics, 147(2):295–328, 1992.

Characters and fusion rules of boundary W-algebras Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction.Communications in mathematical physics, 147(2):295–328, 1992

Reference 26

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Observation 8c5acc62-6a84-493d-be6c-f861941e834d · outbound

This paper cites Vertex operator algebras associated to representations of affine and Virasoro algebras.Duke Mathematical Journal, 66(1):123–168, 1992.

Characters and fusion rules of boundary W-algebras Vertex operator algebras associated to representations of affine and Virasoro algebras.Duke Mathematical Journal, 66(1):123–168, 1992

Reference 27

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Observation 7e3bb1c1-d492-4558-aeed-fb91362f0038 · outbound

This paper cites Modular data for the extended Haagerup subfactor.Communications in Mathematical Physics, 356:981–1015, 2017.

Characters and fusion rules of boundary W-algebras Modular data for the extended Haagerup subfactor.Communications in Mathematical Physics, 356:981–1015, 2017

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Observation bec779fb-6724-4b76-aa51-9b5469235976 · outbound

This paper cites Reduction by stages for affine W-algebras.

Characters and fusion rules of boundary W-algebras Reduction by stages for affine W-algebras

Reference 29

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Observation a87f1b1c-fdd5-45d2-b936-5645ed21f6cd · outbound

This paper cites Rigidity and modularity of vertex tensor categories.Communications in contemporary mathematics, 10(supp01):871–911, 2008.

Characters and fusion rules of boundary W-algebras Rigidity and modularity of vertex tensor categories.Communications in contemporary mathematics, 10(supp01):871–911, 2008

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Observation 0d0f213e-5d7e-4054-b93f-1e6ab9937500 · outbound

This paper cites Quantum reduction for affine superalgebras.Com- munications in Mathematical Physics, 241, 2003.

Characters and fusion rules of boundary W-algebras Quantum reduction for affine superalgebras.Com- munications in Mathematical Physics, 241, 2003

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Observation 321d0359-3b3b-4575-b396-13a102ca93c1 · outbound

This paper cites Classification of modular invariant representations of affine algebras.

Characters and fusion rules of boundary W-algebras Classification of modular invariant representations of affine algebras

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Observation 3c36aefc-47c7-4216-ad16-05966745430e · outbound

This paper cites Number 10 in University Lecture Series.

Characters and fusion rules of boundary W-algebras Number 10 in University Lecture Series

Reference 33

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Observation df27ab5a-a434-4643-aa72-db6b12ad213c · outbound

This paper cites Infinite-dimensional Lie algebras, theta functions and modular forms.Advances in Mathematics, 53(2):125–264, 1984.

Characters and fusion rules of boundary W-algebras Infinite-dimensional Lie algebras, theta functions and modular forms.Advances in Mathematics, 53(2):125–264, 1984

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Observation 5208e4ff-613c-40ff-890b-1f33a991ead6 · outbound

This paper cites Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.Proceedings of the National Academy of Sciences, 85(14):4956–4960, 1988.

Characters and fusion rules of boundary W-algebras Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.Proceedings of the National Academy of Sciences, 85(14):4956–4960, 1988

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Observation 50b4649e-2ebf-4c94-92e7-22ef397e0378 · outbound

This paper cites Branching functions for winding subalgebras and tensor products.

Characters and fusion rules of boundary W-algebras Branching functions for winding subalgebras and tensor products

Reference 36

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Observation b856110d-08c6-4b63-a671-fca4da227a70 · outbound

This paper cites On rationality ofW-algebras.Transformation Groups, 13(3):671– 713, 2008.

Characters and fusion rules of boundary W-algebras On rationality ofW-algebras.Transformation Groups, 13(3):671– 713, 2008

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Observation ef4930f4-4687-40af-a53c-01cb87a40a98 · outbound

This paper cites A remark on boundary level admissible representations.Comptes Rendus.

Characters and fusion rules of boundary W-algebras A remark on boundary level admissible representations.Comptes Rendus

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Observation 2c2e5f75-1bc3-4ba6-a1ec-b7278a256524 · outbound

This paper cites Symmetric invariant bilinear forms on vertex operator algebras.Journal of Pure and Applied Algebra, 96(3):279–297, 1994.

Characters and fusion rules of boundary W-algebras Symmetric invariant bilinear forms on vertex operator algebras.Journal of Pure and Applied Algebra, 96(3):279–297, 1994

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Observation b96bc7d1-48e1-40e0-aa09-cf14b94529ba · outbound

This paper cites On rationality forC 2-cofinite vertex operator algebras.

Characters and fusion rules of boundary W-algebras On rationality forC 2-cofinite vertex operator algebras

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Observation 1c891d04-c5b8-4c63-9fa1-eb9d0f3508e8 · outbound

This paper cites Classical and quantum conformal field theory.Communications in Mathematical Physics, 123(2):177–254, 1989.

Characters and fusion rules of boundary W-algebras Classical and quantum conformal field theory.Communications in Mathematical Physics, 123(2):177–254, 1989

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Observation ca626469-0405-464c-afd8-305f0dc69020 · outbound

This paper cites On Bethe equations of 2d conformal field theory.Journal of High Energy Physics, 2024(9):1–105, 2024.

Characters and fusion rules of boundary W-algebras On Bethe equations of 2d conformal field theory.Journal of High Energy Physics, 2024(9):1–105, 2024

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Observation da2bdf86-b06e-4ae3-a8bf-6a4045e64be1 · outbound

This paper cites Cherednik algebras,W-algebras and the equivariant cohomology of the moduli space of instantons onA 2.Publications math´ ematiques de l’IH´ES, 118(1):213–342, 2013.

Characters and fusion rules of boundary W-algebras Cherednik algebras,W-algebras and the equivariant cohomology of the moduli space of instantons onA 2.Publications math´ ematiques de l’IH´ES, 118(1):213–342, 2013

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Observation a96346d1-ffe0-4cec-a8a3-1e170f199b81 · outbound

This paper cites Modularity for $\mathcal{W}$-algebras and affine Springer fibres.

Characters and fusion rules of boundary W-algebras Modularity for $\mathcal{W}$-algebras and affine Springer fibres

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Observation a8a29855-958f-4175-8e34-4fc0a25fd428 · outbound

This paper cites Stanley.Enumerative Combinatorics.

Characters and fusion rules of boundary W-algebras Stanley.Enumerative Combinatorics

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Observation 48de70b2-1501-453b-ac41-ad2708460eee · outbound

This paper cites Some isomorphisms between exceptional W-algebras.

Characters and fusion rules of boundary W-algebras Some isomorphisms between exceptional W-algebras

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Characters and fusion rules of boundary W-algebras Unresolved cited work

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Observation a7cb1b8f-4f26-4cfe-8605-820c52a32755 · outbound

This paper cites Chiral algebra of the Argyres-Douglas theory from M5 branes.Physical Review D, 103(6):065003, 2021.

Characters and fusion rules of boundary W-algebras Chiral algebra of the Argyres-Douglas theory from M5 branes.Physical Review D, 103(6):065003, 2021

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Observation e46f75e5-02c5-41c7-ad4e-68088b2adb23 · outbound

This paper cites Module categories of simple current extensions of vertex operator algebras.Journal of Pure and Applied Algebra, 189(1-3):315–328, 2004.

Characters and fusion rules of boundary W-algebras Module categories of simple current extensions of vertex operator algebras.Journal of Pure and Applied Algebra, 189(1-3):315–328, 2004

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Observation a2de4e59-2b78-449a-8c7e-7a60d0123743 · outbound

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Characters and fusion rules of boundary W-algebras Modular invariance of characters of vertex operator algebras.Journal of the American Mathematical Society, 9(1):237–302, 1996

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Pith citing papers

Observation 5a4fd3cd-d0aa-4b60-9051-d70f0b7090dd · inbound

Generalised 4d Partition Functions and Modular Differential Equations cites this paper.

Generalised 4d Partition Functions and Modular Differential Equations Characters and fusion rules of boundary W-algebras

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Resolution: verified exact; arxiv_id, observed 2026-05-17T02:48:54.474369Z

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