标题： $A_1$椭圆广义球面 DAHA 在$K=2$处的推广 显示英文标题

标题： An Elliptic Generalization of $A_1$ Spherical DAHA at $K=2$

摘要： 我们构造了一个代数，它是$A_1$球面 DAHA 的椭圆推广，在$t=-q^{-K/2}$处作用于其有限维模$K=2$上。我们证明了$PSL(2,\mathbb Z)$通过我们所构造代数的自同构作用，并且通过$3\times 3$阶椭圆函数矩阵显式表示了这些自同构和代数算子。推测这一构造与仿射 Laumon 空间的 K-理论特征之间存在联系。我们指出两个潜在的应用，分别涉及 Felder-Varchenko 函数的$SL(3,\mathbb Z)$对称性以及环面纽结和 Seifert 流形的新椭圆不变量。 显示英文摘要

摘要： We construct an algebra that is an elliptic generalization of $A_1$ spherical DAHA acting on its finite-dimensional module at $t=-q^{-K/2}$ with $K=2$. We prove that $PSL(2,\mathbb Z)$ acts by automorphisms of the algebra we constructed, and provide an explicit representation of automorphisms and algebra operators alike by $3\times 3$ matrices of elliptic functions. A relation of this construction to the K-theory character of affine Laumon space is conjectured. We point out two potential applications, respectively to $SL(3,\mathbb Z)$ symmetry of Felder-Varchenko functions and to new elliptic invariants of torus knots and Seifert manifolds.