DAHAs and skein theory
Quantum Algebra
2021-02-25 v3 Representation Theory
Abstract
We give a skein-theoretic realization of the double affine Hecke algebra of Cherednik using braids and tangles in the punctured torus. We use this to provide evidence of a relationship we conjecture between the classical skein algebra of the punctured torus and the elliptic Hall algebra of Burban and Schiffmann.
Cite
@article{arxiv.1909.11247,
title = {DAHAs and skein theory},
author = {Hugh Morton and Peter Samuelson},
journal= {arXiv preprint arXiv:1909.11247},
year = {2021}
}
Comments
Preliminary version, comments welcome! 25 pages, many figures. V2: added some details, diagrams, comments, and subtracted some typos. V3: simplified arguments in Section 3.3, added some clarifying remarks