Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The b-functions for prehomogeneous vector spaces of commutative
  parabolic type and generalized universal Verma modules   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.

33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph