2003/03/11 by Kenei Suzuki, Suzuki, Kenei
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0303124
28 pages, 5 figures, platex
arxiv created 2003/03/11 · arxiv updated 2009/11/30
Let V(λ) be the irreducible lowest weight Uq(D(N,1))-module with lowest weight λ. Assume λ= n0ω0-∑i=0Nniωi, where ω0 is the fundamental weight corresponding to the unique odd coroot h0, and ni are positive integers. V(λ) is called typical if n0 ≥ 0. In this paper, we construct polarizable crystal bases of V(λ) in the category \cal Oint, which is a class of integrable modules. We also describe the decomposition of the tensor product of typical representations into irreducible ones, using the generalized Littlewood-Richardson rule for Uq(D(N)). We also present analogous results for the quantum superalgebra Uq(B(N,1)).