论文标题
麸皮和达哈代表
Branes and DAHA Representations
论文作者
论文摘要
我们使用Brane量化，研究了$ A_1 $的球形双仿射Hecke代数的表示理论，该代数在曾经拟合的圆环上的平面SL（2，c）连接的模量空间上的拓扑A模型。特别是，我们提供了有限维表示与具有紧凑支持的A型抗抗性之间的明确匹配；结果之一是发现新的有限维度不可兼容的表示。我们开始将A模型的故事嵌入M理论的Brane构造中，与3D/3D通信中使用的故事密切相关；结果，我们确定具有PSL（2，Z）动作的特定有限维表示背后的模块化张量类别。我们使用与五大机构的五个构建结构的进一步连接，继续研究4D n = 2*的库仑分支几何形状和线路运算符代数的关系与双仿射Hecke代数的关系。
Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type $A_1$ in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In particular, we provide an explicit match between finite-dimensional representations and A-branes with compact support; one consequence is the discovery of new finite-dimensional indecomposable representations. We proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, we identify modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action. Using a further connection to the fivebrane system for the class S construction, we go on to study the relationship of Coulomb branch geometry and algebras of line operators in 4d N=2* theories to the double affine Hecke algebra.
