Quantum group \(U_q(A_\ell)\) singular vectors in Poincaré-Birkhoff-Witt basis
type: Item
instance of: scholarly article
title: Quantum group \(U_q(A_\ell)\) singular vectors in Poincaré-Birkhoff-Witt basis
zbMATH Open document ID: 0953.17006
DOI: 10.1023/A:1007688525636
author: M. El Falaki
author: V. K. Dobrev
published in: Letters in Mathematical Physics
publication date: 2001-01-26T00:00:00Z
review text: A singular vector of a Verma module is a non-zero element, annihilated by the positive part of the universal enveloping algebra. In this letter the authors give an explicit expression for singular vectors in Verma modules over the Drinfeld-Jimbo quantum algebra \(U_q(A_l)\) in terms of the Poincaré-Birkhoff-Witt basis and relate them with the expression for these vectors in terms of simple root vectors, obtained by the first author earlier.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 1385241
zbMATH Keywords: quantum group
zbMATH Keywords: singular vector
zbMATH Keywords: Poincaré-Birkhoff-Witt basis
zbMATH Keywords: Verma modules
zbMATH Keywords: simple root vector
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1385241