# Explicit construction of irreducible modules for U_q(gl_n)

## TL;DR

This paper introduces a method to explicitly construct irreducible modules for the quantum group U_q(gl_n) using combinatorial admissible relations, extending finite-dimensional and generic modules.

## Contribution

It provides a systematic construction of irreducible U_q(gl_n)-modules from admissible sets of relations, broadening the understanding of module representations.

## Key findings

- Constructed new families of irreducible modules from admissible relations.
- Unified finite-dimensional and generic modules within this framework.
- Proved that each admissible set yields an irreducible module.

## Abstract

We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set of relations defined in \cite{FRZ}. More precisely, we prove that any admissible set of relations leads to a family of irreducible U_q(gl_n)-modules. Finite dimensional and generic modules are particular cases of this construction.