Abstract
Let G be a connected, reductive algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G). In this paper, we study representations of g with a p-character χ of standard Levi form. When g is of type An,Bn,Cn or Dn, a sufficient condition for the irreducibility of standard parabolic baby Verma g-modules is obtained. This partially answers a question raised by Friedlander and Parshall (1990) in [2]. Moreover, as an application, in the special case that g is of type An or Bn, and χ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen (1999) in [6].
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