Hunziker, Markus.Hartsock, Gail.2013-09-242013-09-242013-082013-09-24http://hdl.handle.net/2104/8834It 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.en-USBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.BGG resolutions.Unitary highest weight modules.ThesisWorldwide access