Howe Duality of Type P

Pub Date : 2024-05-02 DOI:10.1007/s00031-024-09850-7
Nicholas Davidson, Jonathan R. Kujawa, Robert Muth
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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 \(U(\mathfrak {p}(m))\).

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P 型的豪二重性
对于 \(m,n \ge 1\) 而言,我们在烈超代数 \(\mathfrak {p}(m)\) 和 \(\mathfrak {p}(n)\) 之间建立了经典的和分类的豪对偶性。我们还描述了通过生成器和关系的呈现,以及普遍包络上代数 \(U(\mathfrak {p}(m))\) 的 Kostant \(\mathbb {Z}\)-form.
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