Characters of \({\mathcal U}_q(gl(n))\)-reflection equation algebra
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.
scientific article; zbMATH DE number 1785679