The second cohomology of small irreducible modules for simple algebraic groups

Details The second cohomology of small irreducible modules for simple algebraic groups The second cohomology of small irreducible modules for simple algebraic groups

2000-06-14

arxiv.org/abs/math/0006105v3

Pacific J. of Math. 204, 2002, pp. 459--472

Mathematics

Representation Theory

11 pages; includes now a simplified proof, that was pointed out to the Author, of the main result in the case where Lie(G) act

Scientific paper

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 H^1(G,V)=0. In this paper we show that H^2(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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