Article ID Journal Published Year Pages File Type
4585201 Journal of Algebra 2013 21 Pages PDF
Abstract

In this paper we study affine Deligne–Lusztig varieties Xw(b) for GL2 and their étale 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 σ-stabilizer of b, in their étale 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 GL2 of a local field and of its inner form, which is the group of units of a quaternion algebra, occur in the cohomology.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory