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Resolutions and Hilbert series of the unitary highest weight modules of the exceptional groups


Authors: Thomas J. Enright and Markus Hunziker
Journal: Represent. Theory 8 (2004), 15-51
MSC (2000): Primary 22E47, 17B10, 14M12, 13D02
DOI: https://doi.org/10.1090/S1088-4165-04-00215-8
Published electronically: April 15, 2004
MathSciNet review: 2048586
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Thomas J. Enright
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
Email: tenright@math.ucsd.edu

Markus Hunziker
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403
Email: hunziker@math.uga.edu

DOI: https://doi.org/10.1090/S1088-4165-04-00215-8
Keywords: Highest weight modules, minimal resolutions, Hilbert series
Received by editor(s): October 22, 2003
Published electronically: April 15, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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