A note on the tensor product of restricted simple modules for algebraic groups

De Visscher, M. (2006). A note on the tensor product of restricted simple modules for algebraic groups. Journal of Algebra, 303(1), pp. 407-415. doi: 10.1016/j.jalgebra.2005.06.010

Abstract

Let G be a semisimple simply connected algebraic group over an algebraically closed field of positive characteristic p. Denote by G1 its first Frobenius kernel. In this note, we determine for which group G the restriction to G1 of any indecomposable G-summand of the tensor product of any two restricted simple G-modules remains indecomposable.