Frobenius map for the centers of hecke algebras

Jinkui Wan; Weiqiang Wang

doi:10.1090/s0002-9947-2014-06211-9

Frobenius map for the centers of hecke algebras

Jinkui Wan, Weiqiang Wang

数学学院

University of Virginia School of Engineering and Applied Science

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

We introduce a commutative associative graded algebra structureon the direct sum Z of the centers of the Hecke algebras associated to thesymmetric groups in n letters for all n. As a natural deformation of theclassical construction of Frobenius, we establish an algebra isomorphism fromZ to the ring of symmetric functions. This isomorphism provides an identificationbetween several distinguished bases for the centers (introduced byGeck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.

源语言	英语
页（从-至）	5507-5520
页数	14
期刊	Transactions of the American Mathematical Society
卷	367
期	8
DOI	https://doi.org/10.1090/s0002-9947-2014-06211-9
出版状态	已出版 - 2015

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10.1090/s0002-9947-2014-06211-9

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Wan, J., & Wang, W. (2015). Frobenius map for the centers of hecke algebras. Transactions of the American Mathematical Society, 367(8), 5507-5520. https://doi.org/10.1090/s0002-9947-2014-06211-9

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abstract = "We introduce a commutative associative graded algebra structureon the direct sum Z of the centers of the Hecke algebras associated to thesymmetric groups in n letters for all n. As a natural deformation of theclassical construction of Frobenius, we establish an algebra isomorphism fromZ to the ring of symmetric functions. This isomorphism provides an identificationbetween several distinguished bases for the centers (introduced byGeck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.",

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AU - Wang, Weiqiang

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N2 - We introduce a commutative associative graded algebra structureon the direct sum Z of the centers of the Hecke algebras associated to thesymmetric groups in n letters for all n. As a natural deformation of theclassical construction of Frobenius, we establish an algebra isomorphism fromZ to the ring of symmetric functions. This isomorphism provides an identificationbetween several distinguished bases for the centers (introduced byGeck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.

AB - We introduce a commutative associative graded algebra structureon the direct sum Z of the centers of the Hecke algebras associated to thesymmetric groups in n letters for all n. As a natural deformation of theclassical construction of Frobenius, we establish an algebra isomorphism fromZ to the ring of symmetric functions. This isomorphism provides an identificationbetween several distinguished bases for the centers (introduced byGeck-Rouquier, Jones, Lascoux) and explicit bases of symmetric functions.

KW - Centers

KW - Frobenius map

KW - Hecke algebras

KW - Symmetric functions

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Frobenius map for the centers of hecke algebras

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