The -functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules
Atsushi Kamita
Osaka City University, Japan
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Abstract
We shall give a new elementary proof of the uniform expression for the b-functions of prehomogeneous vector spaces of commutative parabolic type obtained by Muller, Rubenthaler and Schiffmann [5] by using micro-local analysis. Our method is similar to 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 [10], Gyoja [1], Wachi [13].
Cite this article
Atsushi Kamita, The -functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 471–495
DOI 10.2977/PRIMS/1145475365