2022/07/13 by Christopher Ryba, Ryba, Christopher
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2207.06319
openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A celebrated result of Farahat and Higman constructs an algebra FH which "interpolates" the centres Z(ℤSn) of group algebras of the symmetric groups Sn. We extend these results from symmetric group algebras to type A Iwahori-Hecke algebras, Hn(q). In particular, we explain how to construct an algebra FHq "interpolating" the centres Z(Hn(q)). We prove that FHq is isomorphic to R[q,q-1] ⊗ℤ Λ (where R is the ring of integer-valued polynomials, and Λ is the ring of symmetric functions). The isomorphism can be described as "evaluation at Jucys-Murphy elements", leading to a proof of a conjecture of Francis and Wang. This yields character formulae for the Geck-Rouquier basis of Z(Hn(q)) when acting on Specht modules.