Kazhdan-Lusztig-type multiplicity formula for symmetrizable generalized Kac-Moody algebras
type: Item
instance of: scholarly article
title: Kazhdan-Lusztig-type multiplicity formula for symmetrizable generalized Kac-Moody algebras
zbMATH Open document ID: 0829.17021
author: Satoshi Naito
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-12-18T00:00:00Z
review text: This is an announcement of the author's following result. Let \({\mathfrak g}(A)\) be a generalized Kac-Moody algebra with a symmetrizable GGCM \(A=(a_{ij})_{i,j\in I}\) satisfying the condition that \(a_{ii}\neq 0\) \((i\in I)\). Let \(\Lambda\in P_+\) and \((w,\beta),(z,\beta)\in W\times A(\Lambda)\), where \(A(\Lambda)\) is a certain subset of an imaginary root lattice. The Verma module \(V((w,\beta)\circ\Lambda)\) and its irreducible quotient \(L((w,\beta)\circ\Lambda)\) are defined and the multiplicity \([V((w,\beta)\circ\Lambda):L((z,\beta)\circ\Lambda)]\) makes sense. The main result says that this multiplicity equals the value at \(q=1\) of the Kazhdan-Lusztig polynomial \(P_{w,z}(q)\).
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 701458
zbMATH Keywords: generalized Kac-Moody algebra
zbMATH Keywords: Verma module
zbMATH Keywords: multiplicity
zbMATH Keywords: Kazhdan-Lusztig polynomials
MaRDI profile type: Publication
full work available at URL: pjaa.70.94
OpenAlex ID: W2027649783
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DOI: 10.3792/PJAA.70.94
description: scientific article; zbMATH DE number 701458