The second cohomology of small irreducible modules for simple algebraic groups

2000/06/30 by George J. McNinch
Mathematics · #math.RT

paper · pdf

published as Pacific J. of Math. 204, 2002, pp. 459--472 · 11 pages; includes now a simplified proof, that was pointed out to the Author, of the main result in the case where Lie(G) acts non-trivially

arxiv created 2000/12/05 · arxiv updated 2009/11/30

Abstract

Let G be a simple, simply connected and connected algebraic group over an algebraically closed field of characteristic p>0, and let V be a rational G-module such that dim V <= p. According to a result of Jantzen, V is completely reducible, and H¹(G,V)=0. In this paper we show that H²(G,V) = 0 unless some composition factor of V is a non-trivial Frobenius twist of the adjoint representation of G.

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