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Introduction: This article will present just one example of a general construction known as the Bernstein-Gelfand-Gelfand (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, 1368-1376 (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.
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