Gaussian concentration of the q-characters of the Hecke algebras of type A

2010/09/22 by Pierre‐Loïc Méliot, Pierre-Loïc Méliot, Méliot, Pierre-Loïc · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Random Matrices and Applications #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1009.4288

10 pages

arxiv created 2010/09/22 · openalex publication_date 2010/09/22 · arxiv updated 2010/09/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We show that with respect to the q-Plancherel measure on partitions of size n, the irreducible characters of an Hecke algebra H_q(S_n) are concentrated around the normalized trace of H_q(S_n). More precisely, we prove that the deviations of the values of the q-characters χ^λ_q are asymptotically gaussian, and we give an explicit formula for the covariances of the limit normal laws (the other results were already in arXiv:1001.2180). Our proof involves Sniady's theory of cumulants of observables of diagrams and a Möbius inversion formula for additive class functions on symmetric groups.

Cited by

• A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra
• Asymptotics of the Gelfand models of the symmetric groups

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