Asymptotics of characters of symmetric groups related to Stanley character formula

Details Asymptotics of characters of symmetric groups related to Stanley character formula Asymptotics of characters of symmetric groups related to Stanley character formula

2007-01-02

arxiv.org/abs/math/0701051v4

Ann. Math. 173 (2011), no. 2, 887-906

Mathematics

Representation Theory

Version 4: Change of title, shortened to 20 pages. Version 3: 24 pages, the title and the list of authors were changed. Versio

Scientific paper

10.4007/annals.2011.173.2.6

We prove an upper bound for characters of the symmetric groups. Namely, we show that there exists a constant a>0 with a property that for every Young diagram \lambda with n boxes, r(\lambda) rows and c(\lambda) columns |Tr \rho^\lambda(\pi) / Tr \rho^\lambda(e)| < [a max(r(\lambda)/n, c(\lambda)/n,|\pi|/n) ]^{|\pi|}, where |\pi| is the minimal number of factors needed to write \pi\in S_n as a product of transpositions. We also give uniform estimates for the error term in the Vershik-Kerov's and Biane's character formulas and give a new formula for free cumulants of the transition measure.

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