Cohomology of SL2 and related structures

Klaus Lux, Nham V. Ngo, Yichao Zhang

Research output: Contribution to journalArticle

Abstract

Let SL2 be an algebraic group defined over an algebraically closed field k of characteristic p > 0. In this paper, we provide a closed formula for dim Hn(SL2, V(m))) for Weyl SL2-modules V(m) when n ≤ 2p − 3. For n > 2p − 3, an exponential bound, only depending on n, is obtained for Hn(SL2, V(m))). Analogous results are also established for the extension spaces ExtnSL2 between Weyl modules V(m1) and V(m2). As a by-product, our results and techniques give explicit upper bounds for the dimensions of cohomology of the Specht modules of symmetric groups, and the cohomology of simple modules of SL2 and the finite group of Lie type SL2(ps)..

Original languageEnglish (US)
Pages (from-to)979-1000
Number of pages22
JournalCommunications in Algebra
Volume46
Issue number3
DOIs
StatePublished - Mar 4 2018

Keywords

  • Algebraic groups
  • Frobenius kernels
  • Weyl module
  • cohomology
  • symmetric groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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