The cohomology of the affine Deligne-Lusztig varieties in the affine flag manifold of $GL_2$

Details The cohomology of the affine Deligne-Lusztig varieties in the affine flag manifold of $GL_2$ The cohomology of the affine Deligne-Lusztig varieties in the affine flag manifold of $GL_2$

2009-10-17

arxiv.org/abs/0910.3342v1

Mathematics

Algebraic Geometry

Scientific paper

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of GL_2. At first we determine all such varieties up to isomorphy. After this we investigate the representations of the sigma-stabilizer of an element b of the group on the etale cohomology of the affine Deligne-Lusztig variety X_w(b). We describe such representations as inductions from compact subgroups and in terms of noncuspidal representations.

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