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

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 ${\chi }_q^{\lambda }$ 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.

10 pages

Cited by in corpus (2)

• 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