Raising/lowering maps and modules for the quantum affine algebra U-q((SI)over-cap(2))

摘要

Let V denote a finite dimensional vector space over an algebraically closed. field. Let U-0 , U-1 , . . . . U-d denote a sequence of nonzero subspaces whose direct sum is V. Let R : V -> V and L : V -> V denote linear transformations with the following properties: for 0 Ud-i and Ld-2i vertical bar Ud-i -> Ud-i . U-i are bijections; the maps R and L satisfy the cubic q-Serve relations where q is nonzero and not a root of unity. Let K : V -> V denote the linear transformation such that (K - q(2i-d)I) U-i = 0 for 0 I-2). We determine which U-q (-> I-2 )- modules arise from our construction.