Affineness of Deligne-Lusztig varieties for minimal length elements

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We prove that the Deligne-Lusztig varieties associated to elements of the
Weyl group which are of minimal length in their twisted class are affine. Our
proof differs from the proof of He and Orlik-Rapoport and it is inspired by the
case of regular elements, which correspond to the varieties involved in
Brou\'e's conjectures.

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