Article ID Journal Published Year Pages File Type
6414761 Journal of Algebra 2014 21 Pages PDF
Abstract

We give a realization of the level zero fundamental representations W(ϖk) of the quantum affine algebra Uq′(g), when g has a maximal parabolic subalgebra of type Cn. We define a semisimple Uq′(g)-module structure on Λ(V)⊗2 in terms of q-deformed Clifford generators, where Λ(V) is the exterior algebra generated by the dual natural representation V of Uq(sln). We show that each W(ϖk) appears in Λ(V)⊗2 (not necessarily multiplicity-free). As a byproduct, we obtain a simple description of the crystal of W(ϖk) in terms of n×2 binary matrices and their (sln,sl2)-bicrystal structure.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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