Extended Deligne-Lusztig varieties for general and special linear groups
Extended Deligne-Lusztig varieties for general and special linear groups
复制标题
一般和特殊线性群的扩展 Deligne-Lusztig 簇
DOI：
10.1016/j.aim.2010.10.010
复制
发表时间：
2011
影响因子：
1.7
通讯作者：
Stasinski A
中科院分区：
文献类型：
--
作者：
Stasinski A
给出了非阿基米德局部域上整数环的有限商上一般线性群和特殊线性群的Deligne-Lusztig变差的推广.以前，Lusztig通过将某些簇附加到Borel子群内的未分支的极大环面上而给出了推广。在本文中，我们将一族所谓的扩展Deligne-Lusztig变种与群的所有驯服分枝极大环面联系起来。此外，我们还分析了各种推广的Deligne-Lusztig簇的结构，并证明了“非分支”簇，包括某种自然推广，一般不能产生所有的不可约表示。另一方面，我们证明了与Lusztig的一些计算相结合的结果表明，对于具有奇数q的Sl2(Fq[ϖ]/(ϖ2))，扩展的Deligne-Lusztig簇确实提供了所有的不可约表示。
We give a generalisation of Deligne–Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties to unramified maximal tori inside Borel subgroups. In this paper we associate a family of so-called extended Deligne–Lusztig varieties to all tamely ramified maximal tori of the group. Moreover, we analyse the structure of various generalised Deligne–Lusztig varieties, and show that the “unramified” varieties, including a certain natural generalisation, do not produce all the irreducible representations in general. On the other hand, we prove results which together with some computations of Lusztig show that for SL2(Fq[ϖ]/(ϖ2)), with odd q, the extended Deligne–Lusztig varieties do indeed afford all the irreducible representations.