Explicit construction of irreducible modules for $$U_q(\mathfrak {gl}_n)$$ U q ( gl n )

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 objectadmissible set of relations. 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.