Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras
Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras
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DOI：
10.1007/s10468-019-09908-1
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通讯作者：
Jinkui Wan
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作者：
Weideng Cui; Jinkui Wan
We explore the modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras. We provide an equivalence between the category of finite dimensional representations of the affine (resp. cyclotomic) Yokonuma-Hecke algebra and that of an algebra which is a direct sum of tensor products of affine Hecke algebras of type A (resp. Ariki-Koike algebras). As one of the applications, the irreducible representations of affine and cyclotomic Yokonuma-Hecke algebras are classified over an algebraically closed field of characteristic p. Secondly, the modular branching rules for these algebras are obtained; moreover, the resulting modular branching graphs for cyclotomic Yokonuma-Hecke algebras are identified with crystal graphs of irreducible integrable representations of affine Lie algebras of type A.
