We give a skein-theoretic realization of the \(\mathfrak {gl}_n\) 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 skein algebra of closed links in the punctured torus and the elliptic Hall algebra of Burban and Schiffmann.

中文翻译：

---

DAHA和Skein理论

我们使用切开的圆环中的辫子和缠结，给出了Cherednik的\（\ mathfrak {gl} _n \）双仿射Hecke代数的弯曲理论实现。我们用它提供证据证明我们猜想了穿孔圆环中闭合链接的丝球代数与Burban和Schiffmann的椭圆霍尔代数之间的关系。