February 25

Charles Conley ( U. North Texas )

Contact vector fields on the superline

Abstract: I will discuss several problems arising from the action of the Lie superalgebra K of contact vector fields on modules of differential operators over the superline. K contains the conformal subalgebra, a copy of osp(1|2). The focus will be on the action of K with respect to the decompositions of the differential operator modules under the action of the conformal subalgebra. There are applications to 1-cohomology, equivalences between subquotients of differential operator modules, and bounded modules of finite length.