A combinatorial property of Bernstein-Gelfand-Gelfand resolutions of unitary highest weight modules.
Date
2013-08
Authors
Hartsock, Gail.
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Worldwide access
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Abstract
It follows from a formula by Kostant that the difference between the highest weights of consecutive parabolic Verma modules in the Bernstein-Gelfand-Gelfand-Lepowsky resolution of the trivial representation is a single root. We show that an analogous property holds for all unitary representations of simply laced type. Specifically, the difference between consecutive highest weights is a sum of positive noncompact roots all with multiplicity one.
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Keywords
BGG resolutions., Unitary highest weight modules.