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

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→Dist(T) obtained by the restriction of the natural map Dist(GL(m|n))→Dist(T). We define supersymmetric elements in Dist(T) and show that each image h(c) for c∈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.