Askey-Wilson polynomial and genus-two skein module

2025/07/02 by Hikami, Kazuhiro
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2507.01665

Abstract

Based on the q-difference operators for the genus-two skein algebra, we show the correspondence between the reduced Askey-Wilson polynomials and the skein module of the genus-two handlebody.

Citations

• A note on double affine Hecke algebra for skein algebra on twice-punctured torus
• Generalized Double Affine Hecke Algebra for Double Torus
• DAHAs and skein theory
• Affine cubic surfaces and character varieties of knots
• DAHA-Jones polynomials of torus knots
• Jones polynomials of torus knots via DAHA
• Double affine Hecke algebras of rank 1 and affine cubic surfaces
• Askey-Wilson polynomials: an affine Hecke algebraic approach

Related

• Higher Rank Askey-Wilson Algebras as Skein Algebras
• The factorization method for the Askey-Wilson polynomials.
• Higher Skein Modules
• Askey-Wilson polynomials: an affine Hecke algebraic approach
• Algorithms for Skein Manipulation in a Genus-2 Handlebody