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

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

2007-12-11

arxiv.org/abs/0712.1780v3

J. reine angew. Math. 633 (2009), 115-163

Mathematics

Representation Theory

48 pages

Scientific paper

10.1515/CRELLE.2009.062

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.

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