2023/08/26 by Santosha Pattanayak, Pattanayak, Santosha, Preena Samuel +1
Mathematics · #14M30 #17B10 #17B35 #17B65 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2308.13930
openalex publication_date 2023/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the mixed tensor space of a \mathbb Z2-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, these turn out to be the supertrace monomials which is analogous to the results of Procesi in the classical case. A queer supergroup analogue of these results is also obtained.