A note on irreducible representations of symmetric groups and Sergeev superalgebras

TL;DR

This paper presents explicit constructions and a closed-form dimension formula for irreducible representations of symmetric groups and Sergeev superalgebras over fields of positive characteristic.

Contribution

It provides a new explicit construction and a dimension formula in terms of hook lengths for these irreducible representations.

Findings

Derived a closed dimension formula using hook lengths.

Constructed explicit models for irreducible representations.

Applicable over algebraically closed fields of characteristic p>0.

Abstract

We provide an explicit construction and a closed dimension formula in terms of hook lengths for the irreducible representations for the symmetric groups $\mathfrak{S}_p$ and the Sergeev superalgebras $\mathcal{Y}_p$ over an algebraically closed field $\mathbb{F}$ of characteristic $p>0$.