JournalsprimsVol. 41, No. 2pp. 471–495

The <em>b</em>-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules

  • Atsushi Kamita

    Osaka City University, Japan
The <em>b</em>-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules cover
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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 <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. 471–495

DOI 10.2977/PRIMS/1145475365