论文标题
Hecke代数字符的几何方法
A geometric approach to characters of Hecke algebras
论文作者
论文摘要
对于连接的，简单连接的半神经复合代数G组的任何元素，以及相应的Weyl组的元素的选择，都有相关的lusztig品种。当G的元素是常规的半神经时，相应的品种将带有Weyl群在其（e术）相交共同体学上的作用。通过此动作，我们恢复相应Hecke代数的Kazhdan-Lusztig基础的元素的感应特征。在A型中，我们证明了一个更精确的说明：此动作的Frobenius特征恰恰是由Kazhdan-Lusztig基元元素的字符给出的对称函数。主要思想是找到这些品种降落化的分解，并应用Brosnan-Chow pleindromicity标准来确定何时局部不变循环图何时是同构。 这恢复了有关角色束带的Lusztig的一些结果，并将Brosnan-Chow解决方案的概括性概括为涉及奇异性的非二分位排列的股份猜想。我们还审查了内在的，Hecke代数和无差异图的彩色准对称函数之间的连接。
To any element of a connected, simply connected, semisimple complex algebraic group G and a choice of an element of the corresponding Weyl group there is an associated Lusztig variety. When the element of G is regular semisimple, the corresponding variety carries an action of the Weyl group on its (equivariant) intersection cohomology. From this action, we recover the induced characters of an element of the Kazhdan-Lusztig basis of the corresponding Hecke algebra. In type A, we prove a more precise statement: that the Frobenius character of this action is precisely the symmetric function given by the characters of a Kazhdan-Lusztig basis element. The main idea is to find celular decompositions of desingularizations of these varieties and apply the Brosnan-Chow palindromicity criterion for determining when the local invariant cycle map is an isomorphism. This recovers some results of Lusztig about character sheaves and gives a generalization of the Brosnan-Chow solution to the Sharesian-Wachs conjecture to non-codominant permutations, where singularities are involved. We also review the connections between Immanants, Hecke algebras, and Chromatic quasisymmetric functions of indifference graphs.
