Séminaire Lotharingien de Combinatoire, B50d (2004), 11 pp.

Richard P. Stanley

Irreducible Symmetric Group Characters of Rectangular Shape

Abstract. We give a new formula for the values of the symmetric group characters indexed by a rectangular shape. In the second part, we investigate the nature of the values of symmetric group characters indexed by arbitrary shapes. We show that, after appropriate normalization, these are polynomials in parameters that naturally encode the shapes, and we present a conjecture pertaining to the sign of the coefficients of these polynomials.

Received: October 29, 2003. Accepted: January 17, 2004. Final Version: February 13, 2004.

The following versions are available: