On the tensor product of two basic representations of Uᵥ(slₑ)

الأصل · EN

Let {B(Λₘ)|m∈/e} be the set of level one g(A⁽¹⁾ₑ₋₁)-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).