Quantum Berezinian and the classical Capelli identity
type: Item
instance of: scholarly article
title: Quantum Berezinian and the classical Capelli identity
zbMATH Open document ID: 0722.17004
DOI: 10.1007/BF00401646
author: Maxim Nazarov
published in: Letters in Mathematical Physics
publication date: 1991-01-01T00:00:00Z
review text: For the quantum deformation of the Lie superalgebra \({\mathfrak gl}(m| n)\) the analogue of the determinant - quantum Berezinian - is constructed by a new method leading to a ``super'' analog of the Capelli identity and a conjectorial description of the center of \(U_ q({\mathfrak gl}(m| n))\). The proof, based on a (quantum, super) version of Howe's duality, is to be published.
reviewed by: Dimitry Leites
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 4189969
zbMATH Keywords: quantum groups
zbMATH Keywords: quantum deformation
zbMATH Keywords: Lie superalgebra
zbMATH Keywords: quantum Berezinian
zbMATH Keywords: Capelli identity
MaRDI profile type: Publication
cites work: The Yangians, Bethe Ansatz and combinatorics
cites work: Q3361250
cites work: Multiparametric quantum deformation of the general linear supergroup
cites work: A new interpretation of Gelfand-Tsetlin bases
cites work: Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras
description: scientific article; zbMATH DE number 4189969