Howe Duality of Type P

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