Graded picture invariants and polynomial invariants for mixed tensor superspaces

In this paper we consider the mixed tensor space of a Z 2- graded vector space. We obtain a spanning set of invariants of the associated symmetric algebra under the action of the general linear supergroup as well as the queer supergroup over the Grassmann algebra. As a consequence, we give a generating set of polynomial invariants for the simultaneous adjoint action of the general linear supergroup on several copies of its Lie superalgebra. We show that in this special case, this set turns out to be the set of supertrace monomials, which is analogous to the result of Procesi for the general linear group. A queer supergroup analogue of these results is also obtained. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.