Conformal symbols and the action of contact vector fields over the superline

Abstract

Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols, 1-cohomology, and various uniserial subquotients of these modules. We also outline the computation of the K-equivalences and symmetries of their subquotients.

48 pages

References in corpus (3)

• Differential operators on supercircle: conformally equivariant quantization and symbol calculus
• Cohomology of the Lie Superalgebra of Contact Vector Fields on ${\mathbb{R}}^{1|1}$ and Deformations of the Superspace of Symbols
• On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$

Cited by in corpus (6)

• Quantizations of modules of differential operators
• Symmetric Spaces in Supergravity
• The Binary Invariant Differential Operators on Weighted Densities on the superspace ${\mathbb{R}}^{1|n}$ and Cohomology
• Second-Order Conformally Equivariant Quantization in Dimension 1|2
• Differential Operators on the Weighted Densities on the Supercircle $S^{1|n}$
• The Binary $\mathfrak{aff}(n|1)$-Invariant Differential Operators On Weighted Densities On The Superspace ${\mathbb{R}}^{1|n}$ And $\mathfrak{aff}(n|1)$-Relative Cohomology