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

Enright, Thomas; Hunziker, Markus

doi:10.1090/S1088-4165-04-00215-8

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

Represent. Theory 8 (2004), 15-51

DOI: https://doi.org/10.1090/S1088-4165-04-00215-8

Published electronically: April 15, 2004

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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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