Verma modules and differential conformal invariants. (English) Zbl 0732.53011

Baston, R. J.

J. Differ. Geom. 32, No. 3, 851-898 (1990).

From the author’s abstract: “A distinguished class of differential invariants of conformal structures is constructed using homomorphisms of Verma modules and Cartan’s conformal connection. This class reduces to a large subset of the class of differential operators invariant by conformal translation on flat conformal manifolds, and operators in it may be expressed in terms of the Levi-Civita connection and the Ricci curvature of a metric on the conformal class. Composition of these differential operators yields further differential invariants which depend on the conformal curvature.

Reviewer: A.Verona (Los Angeles)

MSC:

53A30	Conformal differential geometry (MSC2010)
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
22E47	Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
58J70	Invariance and symmetry properties for PDEs on manifolds

Keywords:

differential invariants; conformal structures; Verma modules; conformal connection; differential operators