On the tensor product of two basic representations of U_v(sl_e)

2006/06/02 by Susumu Ariki, Ariki, Susumu, Victor Kreiman +3
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0606044

52 pages, (v2,v3) typos and reference numbers corrected, (v4,v5) minor revision

arxiv created 2007/12/20 · arxiv updated 2009/12/01

Abstract

Let \B(Λ_m)|m∈\Z/e\Z\ be the set of level one \mathfrakg(A⁽¹⁾_e-1)-crystals, and consider the realization of B(Λ_m) using e-restricted partitions. We prove a purely Young diagrammatic criterion for an element of B(Λ₀)^{⊗ d₁}⊗ B(Λ_m)^{⊗ d₂} to be in the component B(d₁Λ₀+d₂Λ_m). As an application, we give a non-recursive characterization of simple modules of the Hecke algebra of type B. In the course of the proof, we also obtain a combinatorial description of the second type of Kashiwara's Demazure crystal in B(Λ_m).

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