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Resolutions and Hilbert series of the unitary highest weight modules of the exceptional groups
Author(s):
Thomas
J.
Enright;
Markus
Hunziker
Journal:
Represent. Theory
8
(2004),
15-51.
MSC (2000):
Primary 22E47, 17B10, 14M12, 13D02
Posted:
April 15, 2004
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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.
References:
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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:
10.1090/S1088-4165-04-00215-8
PII:
S 1088-4165(04)00215-8
Keywords:
Highest weight modules,
minimal resolutions,
Hilbert series
Received by editor(s):
October 22, 2003
Posted:
April 15, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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