Equality of multiplicity free skew characters

TL;DR

This paper characterizes when two skew diagrams produce the same multiplicity free skew characters, showing that this occurs only in trivial cases or under specific conjugation conditions.

Contribution

It provides a complete classification of equality cases for multiplicity free skew characters in terms of diagram transformations and conjugation.

Findings

Equality of multiplicity free skew characters occurs only in trivial cases or when diagrams are conjugate staircases.

The paper identifies specific geometric and combinatorial conditions for skew diagram equivalence.

Results clarify the structure of multiplicity free skew characters in representation theory.

Abstract

In this paper we show that two skew diagrams lambda/mu and alpha/beta can represent the same multiplicity free skew character [lambda/mu]=[alpha/beta] only in the the trivial cases when lambda/mu and alpha/beta are the same up to translation or rotation or if lambda=alpha is a staircase partition lambda=(l,l-1,...,2,1) and lambda/mu and alpha/beta are conjugate of each other.