Resolutions and Hilbert series of the unitary highest weight modules of the exceptional groups
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 by Thomas J. Enright and Markus Hunziker PDF
 Represent. Theory 8 (2004), 1551 Request permission
Abstract:
We give a sufficient criterion on a highest weight module of a semisimple Lie algebra to admit a resolution in terms of sums of modules induced from a parabolic subalgebra. In particular, we show that all unitary highest weight modules admit such a resolution. As an application of our results we compute (minimal) resolutions and explicit formulas for the Hilbert series of the unitary highest weight modules of the exceptional groups.References

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Additional Information
 Thomas J. Enright
 Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 920930112
 Email: tenright@math.ucsd.edu
 Markus Hunziker
 Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 306027403
 MR Author ID: 601797
 Email: hunziker@math.uga.edu
 Received by editor(s): October 22, 2003
 Published electronically: April 15, 2004
 © Copyright 2004 American Mathematical Society
 Journal: Represent. Theory 8 (2004), 1551
 MSC (2000): Primary 22E47, 17B10, 14M12, 13D02
 DOI: https://doi.org/10.1090/S1088416504002158
 MathSciNet review: 2048586