Askey-Wilson polynomial and genus-two skein module

TL;DR

This paper establishes a connection between Askey-Wilson polynomials and the genus-two skein module using q-difference operators, revealing new insights into the algebraic structure of skein modules.

Contribution

It introduces a novel correspondence between Askey-Wilson polynomials and the genus-two skein module through q-difference operators.

Findings

Demonstrates the correspondence between Askey-Wilson polynomials and genus-two skein module.

Uses q-difference operators to establish the connection.

Provides a new algebraic perspective on skein modules.

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.