The fundamental representation of the affine Lie algebra \(A_{n-1}^{(1)}\) and the Feynman path integral
type: Item
instance of: scholarly article
title: The fundamental representation of the affine Lie algebra \(A_{n-1}^{(1)}\) and the Feynman path integral
zbMATH Open document ID: 0874.17030
author: Mitsuto Hamada
author: Hiroaki Kanno
author: Kazunori Ogura
author: Kiyosato Okamoto
author: Yuichiro Togoshi
published in: Hiroshima Mathematical Journal
publication date: 1996-09-04T00:00:00Z
review text: In a series of previous works carried out by the authors' group, some Feynman path integrals on the coadjoint orbits of noncompact Lie groups are computed [e.g., \textit{T. Hashimoto}, Hiroshima Math. J. 23, 607-627 (1993; Zbl 0838.22011)]. They showed that the path integrals give the kernel functions of the irreducible unitary representations. Their next problem is to carry out this idea to infinite dimensional Lie groups, where one encounters a new difficulty of nonexistence of the quasi-invariant measure on the coadjoint orbits. However, it is known that the irreducible representations of certain Kac-Moody Lie groups are realized by using the complex white noise on a coadjoint orbit. In this paper the authors utilize this fact for constructing the fundamental representation of the affine Kac-Moody Lie algebra \(A^{(1)}_{n-1}\) by means of the path integral.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 81S40
zbMATH DE Number: 897343
zbMATH Keywords: Feynman path integrals
zbMATH Keywords: infinite dimensional Lie groups
zbMATH Keywords: Kac-Moody Lie groups
zbMATH Keywords: complex white noise
zbMATH Keywords: fundamental representation
zbMATH Keywords: affine Kac-Moody Lie algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127498
OpenAlex ID: W1535603015
Wikidata QID: Q115222441
DOI: 10.32917/HMJ/1206127498
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description: scientific article; zbMATH DE number 897343