On the cocenter of the cyclotomic Hecke algebra of type G(r,1,n)

2022/11/14 by Jun Hu, Lei Shi, Hu, Jun +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.07069

openalex publication_date 2022/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct some integral bases for the cocenter of the cyclotomic Hecke algebra \mathscrH_n,K of type G(r,1,n) by generalizing Geck and Pfeiffer's work on the cocenters of the Iwahori-Hecke algebras associated to finite Weyl groups. We show that the dimensions of both the cocenter and the center of the cyclotomic Hecke algebra \mathscrH_n,K are independent of the characteristic of the ground field, its Hecke parameter and cyclotomic parameters. As applications, we verify Chavli-Pfeiffer's conjecture on the polynomial coefficient g_w,C for the complex reflection group of type G(r,1,n) and also show that both the cocenters and the centers of certain cyclotomic KLR algebras of affine type A are independent of the characteristic of the ground field.

Cited by

• Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras

Related

• On the cyclotomic Hecke algebras of complex reflection groups
• On the centre of the cyclotomic Hecke algebras of G(m,1,2)
• Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras
• Blocks and families for cyclotomic Hecke algebras
• Rouquier blocks of the cyclotomic Hecke algebras of G(de,e,r)