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

TL;DR

This paper introduces new irreducible Gelfand-Tsetlin modules for quantum gl_n with arbitrary singularity and multiplicities up to 2, expanding the class of known modules and including classical cases.

Contribution

It constructs a broad family of irreducible modules for U_q(gl_n) with bounded multiplicities, generalizing previous results and applicable to the classical case q=1.

Findings

Constructed irreducible modules with multiplicity up to 2

Extended the class of known Gelfand-Tsetlin modules

Applicable to both quantum and classical gl_n

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}.