Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras
Modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras
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仿射和分圆横沼-赫克代数的模表示论
DOI：
10.1007/s10468-019-09908-1
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发表时间：
--
影响因子：
0.6
通讯作者：
Jinkui Wan
中科院分区：
文献类型：
--
作者：
Weideng Cui;Jinkui Wan
我们探索仿射和分圆 Yokonuma-Hecke 代数的模表示理论。我们提供了仿射（或分圆）Yokonuma-Hecke 代数的有限维表示范畴与 A 型仿射 Hecke 代数（或 Ariki-Koike 代数）的张量积的直和代数之间的等价关系。作为应用之一，仿射和分圆 Yokonuma-Hecke 代数的不可约表示在特征 p 的代数闭域上进行分类。其次，得到这些代数的模分支规则；此外，所得到的分圆 Yokonuma-Hecke 代数的模分支图可以用 A 型仿射李代数的不可约可积表示的晶体图来识别。
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 typeA(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 characteristicp. 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 typeA.