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

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Date

2021

Author

Ozden, Safak

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Citation

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

Abstract

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.

Source

Journal of Algebra

Volume

572

URI

https://doi.org/10.1016/j.jalgebra.2020.12.019
https://hdl.handle.net/20.500.12713/1350

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  • Makale Koleksiyonu [4]
  • Scopus İndeksli Yayınlar Koleksiyonu [709]
  • WoS İndeksli Yayınlar Koleksiyonu [774]



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