Jucys-Murphy Elements and a Combinatorial Proof of an Identity of S. Kerov
Combinatorics
2010-04-27 v1 Representation Theory
Abstract
Consider the elements of the group algebra CS_{n} given by R_{j}=Sigma_{i=1}^{j-1}(ij), for 2<=j<=n. Jucys [3 - 5] and Murphy[7] showed that these elements act diagonally on elements of S_{n} and gave explicit formulas for the diagonal entries. As requested by the late S. Kerov, we give a combinatorial proof of this work in case j=n and present several similar results which arise from these combinatorial methods.
Keywords
Cite
@article{arxiv.1004.4571,
title = {Jucys-Murphy Elements and a Combinatorial Proof of an Identity of S. Kerov},
author = {Jennifer R. Galovich},
journal= {arXiv preprint arXiv:1004.4571},
year = {2010}
}