Irreductible Representations of the Simple Jordan Superalgebra of Grassmann Poisson bracket

TL;DR

This paper classifies all irreducible bimodules over the Jordan superalgebra $Kan(n)$, extending previous results to all $n \\geq 2$ and fields with characteristic not equal to 2, providing a comprehensive understanding of its module structure.

Contribution

It generalizes prior classifications of irreducible bimodules over $Kan(n)$ to all $n \\geq 2$ and fields with characteristic not 2, filling a gap in the literature.

Findings

Complete classification of irreducible bimodules for all $n \\geq 2$

Extension of results to fields with characteristic not equal to 2

Generalization of previous work for $n>4$ and characteristic zero

Abstract

We obtain classification of the irreducible bimodules over the Jordan superalgebra $Kan(n)$, the Kantor double of the Grassmann Poisson superalgebra $G_n$ on $n$ odd generators, for all $n \geq 2$ and an algebraically closed field of characteristic $\ne 2$. This generalizes the corresponding result of C.Mart\'inez and E.Zelmanov announced in \cite{MZ2} for $n>4$ and a field of characteristic zero.}