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

[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.

[发布日期] 2004-12-01

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