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Stable Centres II: Finite Classical Groups

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arxiv 2112.01467 v1 pith:37XU2U7C submitted 2021-12-02 math.RT math.GRmath.RA

Arun S. Kannan , Christopher Ryba This is my paper · ORCID
classification math.RTmath.GRmath.RA
keywords mathbbalgebracentresconstantsmathrmpolynomialstructurealgebras
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abstract

Farahat and Higman constructed an algebra $\mathrm{FH}$ interpolating the centres of symmetric group algebras $Z(\mathbb{Z}S_n)$ by proving that the structure constants in these rings are "polynomial in $n$". Inspired by a construction of $\mathrm{FH}$ due to Ivanov and Kerov, we prove for $G_n = GL_n, U_n, Sp_{2n}, O_n$, that the structure constants of $Z(\mathbb{Z}G_n(\mathbb{F}_q))$ are "polynomial in $q^n$", allowing us to construct an equivalent of the Farahat-Higman algebra in each case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classical interpolation categories

    math.RT 2025-07 conditional novelty 7.0 of 10

    Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.

  2. Stability of the centers of group algebras of general affine groups $GA_n(q)$

    math.RT 2025-06 conditional novelty 6.0 of 10

    The graded center of Z[GA_n(q)] has n-independent structure constants at maximal reflection length, yielding a universal stable center G(q).

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