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

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

2010-09-22

arxiv.org/abs/1009.4288v1

Mathematics

Representation Theory

10 pages

Scientific paper

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 $\chi^\lambda_q$ 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 M\"obius inversion formula for additive class functions on symmetric groups.

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