Extensions of modules for SL(2,K)

[摘要] In this paper, we consider the induced modules del and the Weyl modules Delta for the algebraic group G = SL(2, K) where K is an algebraically closed field of characteristic p > 0. We determine the G-modules H-i (G(1), del (s) circle times del (t)) for all i greater than or equal to 0, where G(1) is the first Frobenius kernel of G. We then use it to find the Ext(1)-spaces between twisted tensor products of Weyl modules and induced modules for G. Moreover, we describe explicitly the non-split extensions corresponding to del's. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-08-15

[关键词] special linear group;symmetric powers;decomposition matrix