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  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 , Gyoja , Wachi .
Cite this article
Atsushi Kamita, The <em>b</em>-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 471–495DOI 10.2977/PRIMS/1145475365