2024/08/30 by Kazuhiro Hikami, Hikami, Kazuhiro · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2408.17021
openalex publication_date 2024/08/30 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28
We construct a generalization of the C^\vee C1-type double affine Hecke algebra for the skein algebra on the twice-punctured torus Σ1,2 using the Heegaard dual of the Iwahori--Hecke operator recently introduced in our previous article. We show that the automorphisms of our algebra correspond to the Dehn twists about the curves on Σ1,2. We also give the cluster algebraic construction of the the classical limit of the skein algebra, where the Dehn twists are given in terms of the cluster mutations.