Howe Duality of Type P

Abstract

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