Eigenvalues of the Adin-Roichman Matrices

TL;DR

This paper determines the eigenvalues of specific Walsh-Hadamard type matrices related to symmetric group character formulas and descent sets, providing new spectral insights into these combinatorial structures.

Contribution

It explicitly computes the spectrum of the Adin-Roichman matrices, a novel result connecting matrix spectra with symmetric group combinatorics.

Findings

Eigenvalues of Adin-Roichman matrices are explicitly determined.

Spectral properties relate to character formulas and descent sets.

Provides new tools for analyzing symmetric group representations.

Abstract

We find the spectrum of the Walsh-Hadamard type matrices defined by R.Adin and Y.Roichman in their recent work on character formulas and descent sets for the symmetric group.