An introduction to Bernstein-Gelfand-Gelfand sequences
Andreas Cap
(University of Vienna)
Abstract:
I will start by describing a geometric construction of the generalized
Bernstein-Gelfand-Gelfand resolutions on a generalized flag manifold
in terms of invariant differential operators. Next I will discuss how this
construction extends to manifolds endowed with Cartan geometries modelled
on these homogeneous spaces, the so--called parabolic geometries. This not
only provides a general construction for a large class of invariant
differential operators for these geometries but it also leads to an efficient
calculus. Some applications will be discussed in a second lecture on June 23.