Stability of the centers of the symplectic groups rings \matbbZ[Sp_2n(q)]

2018/12/11 by Şafak Özden, Ozden, Safak
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1812.04720

openalex publication_date 2018/12/11 · openalex created_date 2018/12/22 · openalex updated_date 2026/07/28

Abstract

We investigate the structure constants of the center H_n of the group algebra Sp_n(q) over a finite field. The reflection length on the group GL_2n(q) induces a filtration on the algebras H_n. We prove that the structure constants of the associated filtered algebra S_n are independent of n. As a technical tool in the proof, we determine the growth of the centralizers under the embedding Sp_m(q)⊂ Sp_m+l(q) and we show that the index of the centralizer of g∈ Sp_m(q) in the centralizer of g∈ Sp_m+k is equal to q^2ld|Sp_r+l(q)||Sp_r(q)|^-1 for some d and r which are uniquely determined by the conjugacy class of g in GL_2n(q).

Related

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