Abstract
ABSTRACTLet G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q = pr. Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight λ. In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for λ.
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