Quantum b-Functions of Prehomogeneous Vector Spaces of Commutative Parabolic Type

Kamita, Atsushi

doi:10.1006/jabr.2001.8916

Cited by 2 publications

(2 citation statements)

References 22 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This lemma is proved by direct calculations for each case. In [3] there are explicit decompositions of quantum counterparts f q,r of f r satisfying the properties of Lemma 7.2. We can get the decomposition (7.1) from the quantum counterpart via q = 1.…”

Section: Irreducibility Of Verma Modulesmentioning

confidence: 99%

The $b$-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules

Kamita

2005

Publ. Res. Inst. Math. Sci.

Self Cite

View full text Add to dashboard Cite

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]. §1. IntroductionIn this paper we deal with the b-functions of the invariants on the flag manifolds G/P . In the case where P is a Borel subgroup, Kashiwara [3] determined the b-functions by using the universal Verma modules. For general parabolic subgroups P we show that b-functions are regarded as generators of ideals defined by universal generalized Verma modules. When the unipotent radical of P is commutative, we determine the generator.Let g be a simple Lie algebra over the complex number field C, and let G be a connected simply-connected simple algebraic group with Lie algebra g. Fix a parabolic subalgebra p of g. We denote the reductive part of p and the nilpotent part of p by l and n respectively. Let L be the subgroup of G

show abstract

Section: Irreducibility Of Verma Modulesmentioning

confidence: 99%

The $b$-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules

Kamita

2005

Publ. Res. Inst. Math. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…T. Tanisaki and his team introduced q-analogs for prehomogeneous vector spaces of commutative parabolic type and found an explicit form of the associated Sato-Bernstein polynomials [18,17,21,16].…”

Section: Introductionmentioning

confidence: 99%

A q-Analog of the Hua Equations

Bershtein,

Sinel'shchikov

2009

Preprint

View full text Add to dashboard Cite

show abstract

Quantum b-Functions of Prehomogeneous Vector Spaces of Commutative Parabolic Type

Abstract: We show that there exist natural q-analogues of the b-functions for the prehomogeneous vector spaces of commutative parabolic type and calculate them explicitly in each case. Our method of calculating the b-functions seems to be new even for the original case q = 1. 

Cited by 2 publications

References 22 publications

The $b$-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules

The $b$-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules

A q-Analog of the Hua Equations

Contact Info

Product

Resources

About