Finite dimensional simple modules of $(q,\mathbf{Q})$-current algebras

Abstract

The $(q,\mathbf{Q})$-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic $q$-Schur algebras. In this paper, we study the $(q,\mathbf{Q})$-current algebra $U_q({\mathfrak{sl}}_n^{⟨\mathbf{Q}⟩}[x])$ associated with the special linear Lie algebra ${\mathfrak{sl}}_n$. In particular, we classify finite dimensional simple $U_q({\mathfrak{sl}}_n^{⟨\mathbf{Q}⟩}[x])$-modules.

58 pages

References in corpus (1)

• On irreducibility of tensor products of evaluation modules for the quantum affine algebra