Cohomology of SL2 and related structures

Abstract

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