Stability of the centers of the symplectic group rings Z[Sp2n(q)]

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Tarih

2021

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Academic Press Inc.

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

We investigate the structure constants of the center Hn of the group algebra Z[Spn(q)] over a finite field. The reflection length on the group GL2n(q) induces a filtration on the algebras Hn. We prove that the structure constants of the associated graded algebra Sn are independent of n. As tool in the proof we consider the embedding Spm?Spn(q) and determine the behavior of the centralizers and intersection of centralizers under the embedding Spm?Spn(q). We determine explicit formulas for rate of the growth of the centralizer of an element U?Spm(q) in terms of dimension of the fixed space of U.

Açıklama

Anahtar Kelimeler

Farahat-Higman Rings, Growth of Centralizers, Spn-Conjugacy Classes, Structure Constants

Kaynak

Journal of Algebra

WoS Q Değeri

Q3

Scopus Q Değeri

Q1

Cilt

572

Sayı

Künye

Özden, Ş. (2020). Stability of the centers of the symplectic group rings Z [Sp2n (q)]. Journal of Algebra.