The center of $Dist(GL(m|n))$ in positive characteristic

TL;DR

This paper investigates the structure of central elements in the distribution algebra of general linear supergroups over fields of positive characteristic, providing explicit computations for the case of $GL(1|1)$.

Contribution

It explicitly computes the center of the distribution algebra of $GL(1|1)$ and analyzes its image under the Harish-Chandra homomorphism, advancing understanding of supergroup centers.

Findings

Explicit description of the center of $Dist(GL(1|1))$

Calculation of the Harish-Chandra homomorphism image

Insights into the structure of distribution algebra centers in positive characteristic

Abstract

The purpose of this paper is to investigate central elements in distribution algebras $Dist(G)$ of general linear supergroups $G=GL(m|n)$. As an application, we compute explicitly the center of $Dist(GL(1|1))$ and its image under Harish-Chandra homomorphism.