Stanley character polynomials

Abstract

Stanley considered suitably normalized characters of the symmetric groups on Young diagrams having a special geometric form, namely multirectangular Young diagrams. He proved that the character is a polynomial in the lengths of the sides of the rectangles forming the Young diagram and he conjectured an explicit form of this polynomial. This Stanley character polynomial and this way of parametrizing the set of Young diagrams turned out to be a powerful tool for several problems of the dual combinatorics of the characters of the symmetric groups and asymptotic representation theory, in particular to Kerov polynomials.

Dedicated to Richard P. Stanley on the occasion of his seventieth birthday

References in corpus (4)

• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• Jack polynomials and free cumulants
• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula

Cited by in corpus (3)

• Polynomial splitting measures and cohomology of the pure braid group
• Linear versus spin: representation theory of the symmetric groups
• Bijection between trees in Stanley character formula and factorizations of a cycle