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

2018/12/24 by František Marko, Marko, Frantisek, Alexandr N. Zubkov +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1812.09963

Abstract

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

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