Symmetric group characters of almost square shape

TL;DR

This paper derives explicit formulas for symmetric group characters associated with nearly square Young diagrams, specifically those shaped as p by p+δ, providing new insights into their algebraic structure.

Contribution

It introduces closed product formulas for irreducible characters of symmetric groups related to almost square Young diagrams, expanding understanding of their combinatorial properties.

Findings

Closed product formulas for characters of almost square shapes

Explicit expressions for p x (p+δ) Young diagrams

Enhanced understanding of symmetric group representations

Abstract

We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+\delta)$ for a fixed value of an integer $\delta$ and an arbitrary integer $p$.