Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4667821 | Advances in Mathematics | 2008 | 59 Pages |
Abstract
Let {B(Λm)|m∈Z/eZ} be the set of level one -crystals, and consider the realization of B(Λm) using e-restricted partitions. We prove a purely Young diagrammatic criterion for an element of B(Λ0)⊗d1⊗B(Λm)⊗d2 to be in the component B(d1Λ0+d2Λm). 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(Λm).
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