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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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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), 15-51 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.
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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
  • 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), 15-51
  • MSC (2000): Primary 22E47, 17B10, 14M12, 13D02
  • DOI: https://doi.org/10.1090/S1088-4165-04-00215-8
  • MathSciNet review: 2048586