Rota, Gian-Carlo; Stein, Joel A. Standard basis in supersymplectic algebras. (English) Zbl 0699.15013 Proc. Natl. Acad. Sci. USA 86, No. 8, 2521-2524 (1989). The authors use combinatorial methods for investigating supersymplectic algebras. A standard basis for products of Pfaffians is found in Theorem 4. Applications on the theory of invariants are obtained; in Theorems 5 and 6 the authors have found the form of weak supersymmetric invariants of the Pfaffian algebra of degree n. In addition, an extension of Weyl’s well-known theorem of the syzygies of the Pfaffian is obtained. Reviewer: P.Koshlukov Cited in 1 ReviewCited in 6 Documents MSC: 15A72 Vector and tensor algebra, theory of invariants 17B45 Lie algebras of linear algebraic groups 20G15 Linear algebraic groups over arbitrary fields Keywords:supersymplectic algebras; theory of invariants; supersymmetric invariants; Pfaffian algebra PDFBibTeX XMLCite \textit{G.-C. Rota} and \textit{J. A. Stein}, Proc. Natl. Acad. Sci. USA 86, No. 8, 2521--2524 (1989; Zbl 0699.15013) Full Text: DOI