Central characters of the symmetric group: σ-vs. Kerov polynomials

Jacob Technion, Amarpreet Rattan
Expressions for the central characters of the symmetric group in terms of polynomials in the symmetric power-sums over the contents of the Young diagram that specifies the irreducible representation ("σ-polynomials") were developed by Katriel (1991, 1996). Expressions in terms of free cumulants that encode the Young diagram ("Kerov polynomials"), were proposed by Kerov (2000). The relation between these procedures is established.