Extensions of modules for SL(2,K)

✍ Scribed by Maud De Visscher

• Book ID: 104140342
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 104 KB
• Volume: 254
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00084-4

✦ Synopsis

In this paper, we consider the induced modules ∇ and the Weyl modules 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 , ∇(s) ⊗ ∇(t)) for all i 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 ∇'s.