Standard Kleshchev Multipartitions and Drinfeld Polynomials of Integral Type
نویسنده
چکیده
By assuming the parameter q ∈ C∗ is not a root of unity and introducing the notion of standard Kleshchev multipartitions, we establish a one-to-one correspondence between standard Kleshchev multipartitions and irreducible representations with integral weights of the affine Hecke algebra of type A. Then, on the one hand, we extend the correspondence to all Kleshchev multipartitions for a given Ariki-Koike algebra of integral type. On the other hand, with the affine quantum Schur–Weyl duality, we further extend this to a correspondence between standard Kleshchev multipartitions and Drinfeld multipolynomials of integral type whose associated irreducible representations determine all irreducible polynomial representations for the quantum loop algebra Uq(ĝln). As an application of this, we identify skew shape representations of the affine Hecke algebra in terms of multisegments and compute the Drinfeld polynomials of their induced skew shape representations of Uq(ĝln).
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