Homology Class of a Deligne-Lusztig variety and its analogues

Abstract

In this paper we consider Deligne-Lusztig varieties and their analogues when the Frobenius endomorphism is replaced with conjugation by an element in a group, especially a regular semisimple or regular unipotent one. We calculate their classes in the Chow group of the flag variety in terms of Schubert classes. Also we give some sufficient criteria when different elements in the Weyl group result in the same class.

arXiv commentfixed a typo in the reference

References in corpus (1)

• From unipotent classes to conjugacy classes in the Weyl group

Cited by in corpus (1)

• Euler characteristic of analogues of a Deligne-Lusztig variety for $G{L}_n$