Gelfand-Tsetlin modules of quantum gl_n$defined by admissible sets of relations

Abstract

The purpose of this paper is to construct new families of irreducible Gelfand-Tsetlin modules for U_q(gl_n). These modules have arbitrary singularity and Gelfand-Tsetlin multiplicities bounded by 2. Most previously known irreducible modules had all Gelfand-Tsetlin multiplicities bounded by 1 \cite{FRZ1}, \cite{FRZ2}. In particular, our method works for q=1 providing new families of irreducible Gelfand-Tsetlin modules for gl_n. This generalizes the results of \cite{FGR3} and \cite{FRZ}.

References in corpus (6)

• Irreducible Generic Gelfand-Tsetlin Modules of $\mathfrak{gl}(n)$
• Geometric approach to $p$-singular Gelfand-Tsetlin ${\mathfrak{gl}}_n$-modules
• Combinatorial construction of Gelfand-Tsetlin modules for ${\mathfrak{gl}}_n$
• Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb{C})$ with arbitrary characters
• De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum gl_N
• Irreducible subquotients of generic gelfand-tsetlin modules over uq(gl(n))