Induction, deformation, and specialization of Lie algebra representations
The authors continue their recent study of non-restricted representations of restricted Lie algebras. In order to achieve results presented here, they provide a sheaf-theoretic formulation of imprimitivity theory which enables them to consider non-affine orbits of the coadjoint representation. They also introduce deformation and specialization of representations which enable them to formulate conjectural relationships between representations of different character types. Two theorems of particular interest are presented: the first is a complete proof of a result formulated by V. Kac concerning the irreducibility of certain induced characters; the second is a proof of a conjecture of V. Kac and B. Weisfeiler concerning the p-divisibility of the dimensions of representations for the restricted Lie algebra of \(SL_ n\).
scientific article; zbMATH DE number 1043
scientific article