Orbits and invariants of the supergroup \(GQ_ n\)
Let \(A\) be a commutative superalgebra with unit over \(\mathbb{C}\) such that \(A/ A_1\oplus (A_1)^2 \simeq \mathbb{C}\), and let \(\pi: A\to \mathbb{C}\) be the corresponding projection. Denote the algebra \(\text{Mat} (n; \mathbb{C})\) by \(Q(n; \mathbb{C})\), the group \(GL (n; \mathbb{C})\) by \(GQ(n; \mathbb{C})\), and to reduce the description of invariants and orbits of \(GQ (n; \mathbb{C})\) to the study of the action of \(S_n\) and \((A_1)^n\) on \(\mathbb{C}^n\), we consider the analogous problems for the action of the supergroup \(GQ_n\) on the supermanifold \(\widetilde {Q}_n\).
scientific article; zbMATH DE number 95230