Asymptotics of characters of symmetric groups: structure of Kerov character polynomials
Abstract
We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the shape of the Young diagram). We show that for each genus there exists a universal symmetric polynomial which gives the coefficients of the part of Kerov character polynomials with the prescribed homogeneous degree. The existence of such symmetric polynomials was conjectured by Lassalle.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2009
- DOI:
- 10.48550/arXiv.0911.1038
- arXiv:
- arXiv:0911.1038
- Bibcode:
- 2009arXiv0911.1038D
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Representation Theory;
- 20C30;
- 05A15
- E-Print:
- Journal of Combinatorial Theory, Series A, 119 (6), 2012, pp 1174-1193