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arXiv · 1506.06570

Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras

Weideng Cui·Jinkui Wan
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Abstract

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 $A.$

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BibTeXRIS

Weideng Cui, Jinkui Wan. 2015-06-22. Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras. https://arxiv.org/abs/1506.06570

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