English

DAHAs and skein theory

Quantum Algebra 2021-02-25 v3 Representation Theory

Abstract

We give a skein-theoretic realization of the gln\mathfrak{gl}_n 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

R2 v1 2026-06-23T11:24:59.278Z