DAHAs and Skein Theory

We give a skein-theoretic realization of the gln\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {gl}_n$$\end{document} 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 skein algebra of closed links in the punctured torus and the elliptic Hall algebra of Burban and Schiffmann.