Summary:

Introduction: This article will present just one example of a general construction known as the BernsteinGelfandGelfand (BGG) resolution. It was the motivating example from two lectures on the BGG resolution given at the 19th Czech Winter School on Geometry and Physics held in Srn\'{\i} in January 1999. This article may be seen as a technical example to go with a more elementary introduction which will appear elsewhere [{\it M. Eastwood}, Notices Am. Math. Soc. 46, No. 11, 13681376 (1999)]. In fact, there were many lectures on various aspects of the BGG resolution given by other participants in the Winter School. In particular, {\it A. \v{C}ap}, {\it J. Slov\'ak} and {\it V. Sou\v{c}ek} presented their recently worked out curved analogue [BGG sequences, ESI Preprint 722] for a general parabolic geometry. (English) 