论文标题
用于一般线性群体iWahori-Spherical形式的本地角色扩展的三角系统
A triangular system for local character expansions of Iwahori-spherical representations of general linear groups
论文作者
论文摘要
对于非架构的一般线性群的伊瓦霍里（Iwahori）球形表示，陈·萨文（Chan-Savin）最近将惠特克（Whittaker）函子表示为限制有限的iwahori-hecke代数模块的同种型成分。我们概括了这种描述主要退化惠特克函子的方法。同时，我们将Murnaghan的Harish-Chandra的公式视为同一模块的Grothendieck集团扩展。 将两种方法通过Zelevinsky的PSH-Elgebras的镜头进行比较，我们获得了角色扩展系数与主脱位Whittaker尺寸之间的显式unitriangular transrix。
For Iwahori-spherical representations of non-Archimedean general linear groups, Chan-Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori-Hecke algebra module. We generalize this method to describe principal degenerate Whittaker functors. Concurrently, we view Murnaghan's formula for the Harish-Chandra--Howe character as a Grothendieck group expansion of the same module. Comparing the two approaches through the lens of Zelevinsky's PSH-algebras, we obtain an explicit unitriangular transition matrix between coefficients of the character expansion and the principal degenerate Whittaker dimensions.
