Dirac operators and the Very Strange Formula for Lie superalgebras

Abstract

Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.

Latex file, 25 pages. A few misprints corrected. To appear in the forthcoming volume "Advances in Lie Superalgebras", Springer INdAM Series

References in corpus (5)

• The variational Poisson cohomology
• Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
• Shifted Yangians and finite W-algebras
• A BGG-type resolution for tensor modules over general linear superalgebra
• Essential variational Poisson cohomology

Cited by in corpus (4)

• The $Z_2\times Z_2$-graded general linear Lie superalgebra
• Classical W-algebras in types A, B, C, D and G
• Reduction method for representations of queer Lie superalgebras
• SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$