An explicit presentation of the centre of the restricted rational Cherednik algebra

2023/01/09 by Niall Hird, Hird, Niall
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.03316

openalex publication_date 2023/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra H_c(S_n\wrℤ/ℓℤ) for a particular choice of parameter c. More precisely, we describe the centre of the indecomposable blocks of H_c(S_n\wrℤ/ℓℤ) in terms of generators and relations. The parameters c for which this presentation is valid are such that the Calogero-Moser space is smooth. Furthermore, we demonstrate how the explicit presentation of the centre of H_c(S_n\wrℤ/ℓℤ) can be directly derived from the set of ℓ-multipartitions of n.

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