论文标题
A型A型Soergel双模型的评估birepentations
Evaluation birepresentations of affine type A Soergel bimodules
论文作者
论文摘要
在本文中，我们使用soergel演算来定义一个单型函子，称为评估函子，从扩展的A型A型A型soergel双模型到有限A型SOERGEL BIMODULES中有界复合物的同型类别。该函子分类了众所周知的评估同构，从扩展的A型A型Hecke代数为有限的A型Hecke代数。通过它，可以拉回任何有限的A型soergel双模型的限制性的三角抑制，从而获得三角分型A型A型soergel双模型的三角抑制。我们表明，如果A型有限的初始birepentation是一种细胞birepentation，则延长仿射A中的评估birepentation具有限制性覆盖物，我们通过详细详细介绍具有亚规定的细胞抑制案例来说明这一点。
In this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounded complexes in finite type A Soergel bimodules. This functor categorifies the well-known evaluation homomorphism from the extended affine type A Hecke algebra to the finite type A Hecke algebra. Through it, one can pull back the triangulated birepresentation induced by any finitary birepresentation of finite type A Soergel bimodules to obtain a triangulated birepresentation of extended affine type A Soergel bimodules. We show that if the initial finitary birepresentation in finite type A is a cell birepresentation, the evaluation birepresentation in extended affine type A has a finitary cover, which we illustrate by working out the case of cell birepresentations with subregular apex in detail.
