|XXXII Workshop on Geometric Methods in Physics||30.06-6.07.2013|
Participants of Workshop
Participants of School
Operator pencils, densities and equivariant geometry
We consider pencil lifting maps from operators on densities of given weight to operator pencils defined on densities of all weights. In general, such a map can be defined and it can be defined uniquely, only on operators of order \leq 2, if we impose a natural condition that the lifting is equivariant with respect to the group of all diffeomorphisms of the base manifold. We explain the geometrical meaning of such a map. Then we analyze the existence and uniqueness of lifting maps defined on operators of all orders in the case if lifting map is equivariant with respect to a smaller group, such as the group of diffeomorphisms preserving volume form, or the group of diffeomorphisms preserving a projective structure.
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