Characters of \({\mathcal U}_q(gl(n))\)-reflection equation algebra
type: Item
instance of: scholarly article
title: Characters of \({\mathcal U}_q(gl(n))\)-reflection equation algebra
zbMATH Open document ID: 1008.17011
DOI: 10.1023/A:1016283527111
published in: Letters in Mathematical Physics
publication date: 2002-08-21T00:00:00Z
review text: Let \(V\) be a complex vector space and \(S\in \text{End}^{\otimes 2}(V)\) a Yang-Baxter operator, satisfying the braid identity \(S_{12}S_{23}S_{12}=S_{23}S_{12}S_{23}\). The author classifies all solutions \(A\in \text{End}(V)\) to the so-called numerical reflection equation \(SA_2SA_2=A_2SA_2S\), where \(A_2=1\otimes A\), in the case, when the braid matrix is associated with the fundamental vector representation of the Drinfeld-Jimbo quantum group \(U_q(gl(n))\). These solutions define one-dimensional representations (characters) of the reflection equation algebra, which is the quotient of \(T(\text{End}^*(V))\) by the ideal associated with the numerical reflection.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1785679
zbMATH Keywords: quantum group
zbMATH Keywords: character
zbMATH Keywords: reflection equation algebra
zbMATH Keywords: fundamental vector
author: Andrey Mudrov
MaRDI profile type: Publication
full work available at URL: a:1016283527111
OpenAlex ID: W2598599999
description: scientific article; zbMATH DE number 1785679