Howe Duality of Type P

TL;DR

This paper establishes classical and categorical Howe dualities between certain Lie superalgebras and provides a presentation and integral form for their universal enveloping superalgebras.

Contribution

It introduces new dualities for Lie superalgebras of type P and describes their algebraic structures in detail.

Findings

Classical Howe duality between rak{p}(m) and rak{p}(n)

Categorical Howe duality established for these superalgebras

Presentation via generators and relations for U(rak{p}(m))

Abstract

We establish classical and categorical Howe dualities between the Lie superalgebras $\mathfrak{p}(m)$ and $\mathfrak{p}(n)$, for $m,n \geq 1$. We also describe a presentation via generators and relations as well as a Kostant $\mathbb{Z}$-form for the universal enveloping superalgebra $U(\mathfrak{p}(m))$.