Matrices, Characters and Descents
Combinatorics
2014-11-20 v3 Representation Theory
Abstract
A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain character formulas are invertible, yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group.
Cite
@article{arxiv.1301.1675,
title = {Matrices, Characters and Descents},
author = {Ron M. Adin and Yuval Roichman},
journal= {arXiv preprint arXiv:1301.1675},
year = {2014}
}
Comments
35 pages, reorganized