The cohomology of Deligne-Lusztig varieties for the general linear group

被引：1

作者：

Orlik, Sascha ^{[1
]}

机构：

[1] Berg Univ Wuppertal, Fachbereich Math & Nat Wissensch C, Gaussstr 20, D-42119 Wuppertal, Germany

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2018年 / 5卷

关键词：

REGULAR ELEMENTS; REDUCTIVE GROUPS; FINITE; REPRESENTATIONS; CHARACTERS;

D O I：

10.1007/s40687-018-0131-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose two inductive approaches for determining the cohomology of Deligne-Lusztig varieties in the case of G = GL(n). The first one uses Demazure compactifications and analyzes the corresponding Mayer-Vietoris spectral sequence. This allows us to give an inductive formula for the Tate twist -1 contribution of the cohomology of a DL-variety. The second approach relies on considering more generally DL-varieties attached to hypersquares in the Weyl group. Here we give explicit formulas for the cohomology of height-one elements.

引用

页数：71