Special functions and infinite-dimensional representations of Lie groups
type: Item
instance of: scholarly article
title: Special functions and infinite-dimensional representations of Lie groups
zbMATH Open document ID: 0663.33005
DOI: 10.1007/BF02570729
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174120
review text: We present a technique for calculating the matrix elements of representations of a Lie group on the universal enveloping algebra and its quotients. These matrix elements are special functions associated to the group. The case of nilpotent groups is discussed particularly. In general we propose this approach as a method of non-commutative generating functions.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 4084069
zbMATH Keywords: operator algebras
zbMATH Keywords: nilpotent groups
author: Ph. Feinsilver
author: R. Schott
MaRDI profile type: Publication
cites work: Q4065692
cites work: Discrete analogues of the Heisenberg-Weyl algebra
cites work: Filtrations and Canonical Coordinates on Nilpotent Lie Groups
cites work: Q5658283
cites work: Q3967718
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
cites work: Quantum deformations of certain simple modules over enveloping algebras
cites work: Lie theory and special functions
cites work: Q4135772
cites work: Q5508372
cites work: On the Poincaré-Birkhoff-Witt theorem
Wikidata QID: Q115392005
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description: scientific article; zbMATH DE number 4084069