Irreducible modules for the quantum affine algebra Uq((sl)over-cap2) and its Borel subalgebra

JOURNAL OF ALGEBRA

卷:282

Article

Benkart, G ; Terwilliger, P

关键词: affine Lie algebra (sl)over-cap(2);    quantum affine algebra;    irreducible module;    tridiagonal pair;   

DOI  :  10.1016/j.jalgebra.2004.08.016

来源: Elsevier

【 摘 要 】

Let U-q (b) denote the standard Borel subalgebra of the quantum affine algebra U-q((sl(2)) over cap). We show that the following hold for any choice of scalars epsilon(0), epsilon(1) from the set {1. - 1}: (i) Let V be a finite-dimensional irreducible U-q(b)-module of type (epsilon(0), epsilon(1)). Then the action of U-q(b) on V extends uniquely to an action of U-q((sl(2)) over cap) on V. The resulting U-q((sl(2)) over cap)-module structure on V is irreducible and of type (epsilon(0), epsilon(1)). (ii) Let V be a finite-dimensional irreducible U-q((sl(2)) over cap)-module of type (epsilon(0), epsilon(1)). When the U-q((sl(2)) over cap )action is restricted to U-q(b), the resulting Uq(b)-module structure on V is irreducible and of type (epsilon(0), epsilon(1)). (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free