The composition series of modules induced from Whittaker modules
type: Item
instance of: scholarly article
title: The composition series of modules induced from Whittaker modules
zbMATH Open document ID: 0956.17004
author: Wolfgang Soergel
author: Dragan Milicic
published in: Commentarii Mathematici Helvetici
publication date: 2001-02-28T00:00:00Z
review text: Let \({\mathfrak g}\) be a semisimple complex Lie algebra and \({\mathfrak n}\) the nilradical of a Borel subalgebra. Write \(U=U({\mathfrak g})\) for the enveloping algebra of \({\mathfrak g}\) and \(Z\) for its center. Choose \(\chi\) a maximal ideal in \(Z\) and \(f\) a character of \({\mathfrak n}\). Denoting by \({\mathbb C}_f\) the corresponding one dimensional representation of \({\mathfrak n}\), consider the \({\mathfrak g}\)-module \[ Y(\chi, f) = U/\chi U \otimes_{U({\mathfrak n})} {\mathbb C}_f. \] Such modules are of finite length. The problem studied in this paper is to compute the composition factors, with multiplicities, of \(Y(\chi, f)\). The problem is solved completely for integral \(\chi\) and partially for other \(\chi\) as well. The main idea is to reduce the problem to the Kazhdan-Lusztig conjectures describing the composition series of Verma modules. This is accomplished by making use of results of McDowell and proving an equivalence of certain natural categories.
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 22E47
zbMATH DE Number: 1129395
zbMATH Keywords: composition factors
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
full work available at URL: s000140050031
OpenAlex ID: W2030415662
DOI: 10.1007/S000140050031
description: scientific article; zbMATH DE number 1129395