Invariant differential operators and BGG sequences in parabolic geometry

Mike Eastwood

Australian National University

Abstract:

Parabolic geometry is modelled on homogeneous spaces of the form G/P where G is a semisimple Lie group and P is a parabolic subgroup. Classical examples include projective and conformal differential geometry. BGG stands for Bernstein, Gelfand, and Gelfand and the BGG complex on projective space is the simplest instance of a classification of invariant differential operators to be explained in these lectures.

Prerequisites for this course are a basic familiarity with differential geometry and Lie groups (more through examples than general theory). Familiarity with the initial chapters of the book by R.Baston and M.Eastwood, "The Penrose transform: its interaction with representation theory" (Oxford Mathematical Monographs, 1989) will be useful, but not required. The article "Invariant operators" by R.Baston and M.Eastwood in "Twistors in mathematics and physics" (London Mathematical Society Lecture Notes 156, Cambridge University Press 1990) is also useful and, for Lie groups and their representations, the book by W.Fulton and J.Harris, "Representation theory: a first course" (Springer 1991) is recommended.