The b-functions for prehomogeneous vector spaces of commutative parabolic type and generalized universal Verma modules

Details The b-functions for prehomogeneous vector spaces of commutative parabolic type and generalized universal Verma modules The b-functions for prehomogeneous vector spaces of commutative parabolic type and generalized universal Verma modules

2002-06-26

arxiv.org/abs/math/0206274v1

Mathematics

Representation Theory

20 pages, LaTeX2e

Scientific paper

We shall give a uniform expression and a uniform calculation for the b-functions of prehomogeneous vector spaces of commutative parabolic type, which were previously calculated by case-by-case analysis. Our method is a generalization of Kashiwara's approach using the universal Verma modules. We shall also give a new proof for the criterion of the irreducibility of the generalized Verma module in terms of b-functions due to Suga, Gyoja, Wachi.

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