The representations of the Lie superalgebra p(3) in prime characteristic

TL;DR

This paper classifies all irreducible modules of the Lie superalgebra p(3) over fields with characteristic greater than 3 and provides explicit character formulas for these modules.

Contribution

It offers a complete classification of irreducible modules and explicit character formulas for p(3) in prime characteristic, advancing understanding of Lie superalgebra representations.

Findings

All irreducible modules of p(3) are classified.

Explicit character formulas for these modules are provided.

The results apply to fields with characteristic p > 3.

Abstract

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.