Howe Duality of Type P

Abstract

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