Parabolic Deligne-Lusztig varieties

Details Parabolic Deligne-Lusztig varieties Parabolic Deligne-Lusztig varieties

2011-10-21

arxiv.org/abs/1110.4863v2

Mathematics

Group Theory

Scientific paper

Motivated by the Brou\'e conjecture on blocks with abelian defect groups for finite reductive groups, we study "parabolic" Deligne-Lusztig varieties and construct on those which occur in the Brou\'e conjecture an action of a braid monoid, whose action on their $\ell$-adic cohomology will conjecturally factor trough a cyclotomic Hecke algebra. In order to construct this action, we need to enlarge the set of varieties we consider to varieties attached to a "ribbon category"; this category is a {\em Garside category}, which plays an important role in our proof, so we devote the first part of our paper to the necessary background on Garside categories.

Affiliated with

Also associated with

No associations

Rating

Parabolic Deligne-Lusztig varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Parabolic Deligne-Lusztig varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parabolic Deligne-Lusztig varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-85858