Article ID Journal Published Year Pages File Type
4667821 Advances in Mathematics 2008 59 Pages PDF
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).

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)