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arXiv · 1812.09963

Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements

Frantisek Marko·Alexandr N. Zubkov
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Abstract

In this paper we investigate the image of the center $Z$ of the distribution algebra $Dist(GL(m|n))$ of the general linear supergroup over a ground field of positive characteristic under the Harish-Chandra morphism $h:Z \to Dist(T)$ obtained by the restriction of the natural map $Dist(GL(m|n))\to Dist(T)$. We define supersymmetric elements in $Dist(T)$ and show that each image $h(c)$ for $c\in Z$ is supersymmetric. The central part of the paper is devoted to a description of a minimal set of generators of the algebra of supersymmetric elements over Frobenius kernels $T_r$.

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Frantisek Marko, Alexandr N. Zubkov. 2018-12-24. Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements. https://arxiv.org/abs/1812.09963

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