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On the Vanishing Ranges for the Cohomology of Finite Groups of Lie Type.

Authors :
Bendel, Christopher P.
Nakano, Daniel K.
Pillen, Cornelius
Source :
IMRN: International Mathematics Research Notices. May2012, Vol. 2012 Issue 12, p2817-2866. 50p.
Publication Year :
2012

Abstract

Let be a finite Chevalley group defined over the field of q=pr elements, and k be an algebraically closed field of characteristic p>0. A fundamental open and elusive problem has been the computation of the cohomology ring . In this paper, we determine initial vanishing ranges, which improves upon known results. For root systems of type An and Cn, the first nontrivial cohomology classes are determined when p is larger than the Coxeter number (larger than twice the Coxeter number for type An with n>1 and r>1). In the process we make use of techniques involving line bundle cohomology for the flag variety G/B and its relation to combinatorial data from Kostant Partition Functions. [ABSTRACT FROM PUBLISHER]

Details

Language :
English
ISSN :
10737928
Volume :
2012
Issue :
12
Database :
Academic Search Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
76535460