The first fundamental theorem of invariant theory for the orthosymplectic super group

Abstract

We give a new proof, inspired by an argument of Atiyah, Bott and Patodi, of the first fundamental theorem of invariant theory for the orthosymplectic super group. We treat in a similar way the case of the periplectic super group. Lastly, the same method is used to explain the fact that Sergeev's super Pfaffian, an invariant for the special orthosymplectic super group, is polynomial.

References in corpus (3)

• Affine walled Brauer algebras
• Invariants of the orthosymplectic Lie superalgebra and super Pfaffians
• Invariant integration on orthosymplectic and unitary supergroups

Cited by in corpus (8)

• First fundamental theorems of invariant theory for quantum supergroups
• The marked Brauer category
• Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra
• Invariants of the orthosymplectic Lie superalgebra and super Pfaffians
• The first and second fundamental theorems of invariant theory for the quantum general linear supergroup
• Diagrammatics for real supergroups
• Invariants of the special orthogonal group and an enhanced Brauer category
• Simplicities of VOAs Associated to Jordan Algebras of Type $B$ and Character Formulas for Simple Quotients