Modular Representation Theory of Affine and Cyclotomic Yokonuma-Hecke Algebras

Weideng Cui; Jinkui Wan

doi:10.1007/s10468-019-09908-1

Modular Representation Theory of Affine and Cyclotomic Yokonuma-Hecke Algebras

Weideng Cui, Jinkui Wan^*

^*Corresponding author for this work

School of Mathematics and Statistics

Shandong University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1659-1682
Number of pages	24
Journal	Algebras and Representation Theory
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s10468-019-09908-1
Publication status	Published - 1 Aug 2020

Keywords

Affine Yokonuma-Hecke algebras
Branching rules
Cyclotomic Yokonuma-Hecke algebras
Modular representations

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10.1007/s10468-019-09908-1

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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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T1 - Modular Representation Theory of Affine and Cyclotomic Yokonuma-Hecke Algebras

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AU - Wan, Jinkui

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N2 - 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.

AB - 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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Modular Representation Theory of Affine and Cyclotomic Yokonuma-Hecke Algebras

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