Highest weight modules and \(b\)-functions of semi-invariants
type: Item
instance of: scholarly article
title: Highest weight modules and \(b\)-functions of semi-invariants
zbMATH Open document ID: 0821.22006
author: Akihiko Gyoja
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-02-01T00:00:00Z
review text: The author gave a criterion for irreducibility of generalized Verma modules in a preceding paper, where the author clarified that the irreducibility is closely connected with the roots of \(b\)-functions of semi-invariants. Thus, in order to judge when the generalized Verma module is irreducible, it is necessary to calculate the \(b\)-functions of semi-invariants. In this paper, the author develops techniques to compute \(b\)-functions and formulates a new conjecture which would eliminate a restriction of the criterion given in the preceding paper. This paper contains many interesting examples of the calculations of holonomy diagrams. They would give us remarkable information on micro-local structure of semi-invariants.
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 716436
zbMATH Keywords: irreducibility of generalized Verma modules
zbMATH Keywords: roots of \(b\)-functions of semi-invariants
zbMATH Keywords: holonomy diagrams
zbMATH Keywords: micro-local structure
reviewed by: Masakazu Muro
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195165904
OpenAlex ID: W2069241085
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DOI: 10.2977/PRIMS/1195165904
description: scientific article; zbMATH DE number 716436