Extensions of modules for SL(2,K)

In this paper, we consider the induced modules and the Weyl modules Δ for the algebraic group G=SL(2,K) where K is an algebraically closed field of characteristic p>0. We determine the G-modules Hi(G1, (s) (t)) for all i 0, where G1 is the first Frobenius kernel of G. We then use it to find the Ext1-spaces between twisted tensor products of Weyl modules and induced modules for G. Moreover, we describe explicitly the non-split extensions corresponding to ʹs.