Pith. sign in

REVIEW 1 cited by

Cluster structure on genus 2 spherical DAHA: seven-colored flower

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2402.16074 v2 pith:EXBYXZZJ submitted 2024-02-25 math.RT math-phmath.MPmath.QA

Semeon Arthamonov , Leonid Chekhov , Philippe Di Francesco , Rinat Kedem , Gus Schrader , Alexander Shapiro , Michael Shapiro This is my paper · ORCID
classification math.RTmath-phmath.MPmath.QA
keywords genusclusteractionclassembeddinggroupmappingtype
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutation type $X_7$. The embedding is equivariant with respect to the action of the mapping class group of the closed surface of genus 2. The cluster realization of the mapping class group action leads to a formula for the coefficient of each monomial in the genus 2 Macdonald polynomial of type $A_1$ as sum over lattice points in a convex polyhedron in 7-dimensional space.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The algebraic modular functor conjecture in type $A_n$ quantum Teichm\"uller theory

    math.QA 2025-09 conditional novelty 8.0 of 10

    The algebraic modular functor conjecture of Fock and Goncharov, that cutting a surface yields a canonical gluing isomorphism of the associated quantum algebras, is proven for type A_n (G = PGL(n+1)).

Pith tools