Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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205, American Mathematical Society, Providence, RI
19 Pith papers cite this work, alongside 678 external citations. Polarity classification is still indexing.
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Defines a one-parameter family of algebras generalizing Schur algebras and proves they are based quasi-hereditary with representation categories that are highest weight subcategories of parabolic category O for gl_n.
Introduces Higgs bundles on the Fargues-Fontaine curve, establishes a BNR correspondence, and shows an injective étale-stack map from B_dR^+-affine Springer fibers to the Hitchin fiber inducing category equivalence on geometric points.
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
Develops an operator-algebraic framework for fusion category symmetries on (1+1)D lattices, proving realization conditions via integer dimensions and fiber functors plus anomaly-enforced gaplessness theorems.
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
Hodge loci in Calabi-Yau sigma models are identified with non-trivial categories of topological defects preserving N=(2,2) SCA and invertible on spectral-flow generators, with CM structure at special points.
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
Proper outerness is automatic for finite index outer endomorphisms of simple C*-algebras, implying automatic freeness for outer actions of unitary tensor categories.
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
Relates the category of quantum Harish-Chandra bimodules at odd roots of unity to affine Soergel bimodules and non-commutative Springer resolution.
Characterizes the strong identity condition for almost-canonically seminormed rings via orthogonal expansions, projectivity of canonical modules, and Morita equivalences from Zhu algebras, equating smoothing to Morita equivalence for CFT-type VOAs.
Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.
The conflated expression graph for an arbitrary permutation has unique min and max elements, and every reduced expression lies on a maximal chain from source to sink.
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
The thesis constructs the étale fundamental group via the étale topology and recovers it alongside topological and motivic versions through Tannakian duality.
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
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Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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Interpolating Schur Algebras
Defines a one-parameter family of algebras generalizing Schur algebras and proves they are based quasi-hereditary with representation categories that are highest weight subcategories of parabolic category O for gl_n.
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Higgs bundles on the Fargues-Fontaine curve
Introduces Higgs bundles on the Fargues-Fontaine curve, establishes a BNR correspondence, and shows an injective étale-stack map from B_dR^+-affine Springer fibers to the Hitchin fiber inducing category equivalence on geometric points.
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
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The disoriented skein and iquantum Brauer categories
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
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An operator algebraic approach to fusion category symmetry on the lattice
Develops an operator-algebraic framework for fusion category symmetries on (1+1)D lattices, proving realization conditions via integer dimensions and fiber functors plus anomaly-enforced gaplessness theorems.
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Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
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Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
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Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Hodge loci in Calabi-Yau sigma models are identified with non-trivial categories of topological defects preserving N=(2,2) SCA and invertible on spectral-flow generators, with CM structure at special points.
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Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
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Properly Outer Actions of Tensor Categories on C$^*$-algebras
Proper outerness is automatic for finite index outer endomorphisms of simple C*-algebras, implying automatic freeness for outer actions of unitary tensor categories.
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On Hecke and asymptotic categories for a family of complex reflection groups
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
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Quantum Harish-Chandra bimodules at roots of unity and affine Hecke category
Relates the category of quantum Harish-Chandra bimodules at odd roots of unity to affine Soergel bimodules and non-commutative Springer resolution.
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On strong identities of almost-canonically seminormed rings
Characterizes the strong identity condition for almost-canonically seminormed rings via orthogonal expansions, projectivity of canonical modules, and Morita equivalences from Zhu algebras, equating smoothing to Morita equivalence for CFT-type VOAs.
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Presentations for categories of crystals
Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.
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The conflated expression graph for an arbitrary permutation
The conflated expression graph for an arbitrary permutation has unique min and max elements, and every reduced expression lies on a maximal chain from source to sink.
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Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
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\'Etale Fundamental Groups -- a geometric and topological approach to fundamental groups in algebraic geometry
The thesis constructs the étale fundamental group via the étale topology and recovers it alongside topological and motivic versions through Tannakian duality.
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ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.