Cohomology of SL2 and related structures

Klaus M 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 (Formula presented.) for Weyl SL2-modules V(m) when n ≤ 2p − 3. For n > 2p − 3, an exponential bound, only depending on n, is obtained for (Formula presented.). Analogous results are also established for the extension spaces (Formula presented.) 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 (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalCommunications in Algebra
DOIs
StateAccepted/In press - Jul 11 2017

Fingerprint

Cohomology
Weyl Modules
Finite Groups of Lie Type
Specht Module
Exponential Bound
Simple Module
Algebraic Groups
Algebraically closed
Symmetric group
Upper bound
Closed

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Cohomology of SL2 and related structures. / Lux, Klaus M; Ngo, Nham V.; Zhang, Yichao.

In: Communications in Algebra, 11.07.2017, p. 1-22.

Research output: Contribution to journalArticle

Lux, Klaus M ; Ngo, Nham V. ; Zhang, Yichao. / Cohomology of SL2 and related structures. In: Communications in Algebra. 2017 ; pp. 1-22.
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