Q1876545
type: Item
instance of: scholarly article
title: Infinite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) related to complex analogs of the Gelfand-Tsetlin patterns and general hypergeometric functions on the Lie group \(\text{GL}(n,\mathbb C)\).
zbMATH Open document ID: 1052.22012
published in: Acta Applicandae Mathematicae
publication date: 2004-08-20T00:00:00Z
review text: In 1950 Gel'fand-Tsetlin bases for irreducible finite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) were introduced by \textit{I. M. Gel'fand} and \textit{M. L. Tsetlin} [Dokl. Akad. Nauk SSSR, N. Ser. 71, 825--828 (1950; Zbl 0037.15301)] and in 1965 their explicit matrix elements were studied by \textit{I. M. Gel'fand} and \textit{M. I. Graev} [Izv. Akad. Nauk SSSR, Ser. Mat. 29, 1329--1356 (1965; Zbl 0139.30701)]. Here it is shown that this procedure still works when complex Gel'fand-Tsetlin \(n\)-patterns are considered. The author studies the infinite-dimensional representations of \(\mathfrak{gl}(n,\mathbb C)\) constructed in this way together with the local representation of the group \(\text{GL}(n,\mathbb C)\) it yields by exponentiation.
reviewed by: Evelyn Weimar-Woods
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 2093656
zbMATH Keywords: Gelfand-Tsetlin basis
zbMATH Keywords: Gelfand-Tsetlin pattern
zbMATH Keywords: representations of Lie groups and Lie algebras
zbMATH Keywords: general hypergeometric functions
Wikidata QID: Q115335125
author: M. I. Graev
MaRDI profile type: Publication
DOI: 10.1023/B:ACAP.0000024196.16709.F6
label: Infinite-dimensional representations of the Lie algebra \(\mathfrak{gl}(n,\mathbb C)\) related to complex analogs of the Gelfand-Tsetlin patterns and general hypergeometric functions on the Lie group \(\text{GL}(n,\mathbb C)\).
description: scientific article; zbMATH DE number 2093656