Cohomology of affine Deligne-Lusztig varieties for
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- 作者：A. Ivanov ivanov@mathi.uni-heidelberg.de
- 关键词：Affine Deligne&ndash ; Lusztig variety ; Affine flag manifold ; Representation theory ; Induced representation
- 刊名：Journal of Algebra
- 出版年：2013
- 出版时间：1 June, 2013
- 年：2013
- 卷：383
- 期：Complete
- 页码：42-62
- 全文大小：332 K
文摘
In this paper we study affine Deligne-Lusztig varieties for and their ¨¦tale coverings. At first, we compute them explicitly, then we determine associated representations of a certain locally-compact group, the group of rational points of the ¦Ò-stabilizer of b, in their ¨¦tale cohomology. Further, we study these representations by determining morphisms into the irreducible representations of the given group. In particular all cuspidal representations of level 0 of of a local field and of its inner form, which is the group of units of a quaternion algebra, occur in the cohomology.