Show simple item record

dc.contributor.authorAl-Faisal, Faisal
dc.date.accessioned2010-08-30 20:45:26 (GMT)
dc.date.available2010-08-30 20:45:26 (GMT)
dc.date.issued2010-08-30T20:45:26Z
dc.date.submitted2010
dc.identifier.urihttp://hdl.handle.net/10012/5421
dc.description.abstractThis thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all the irreducible holomorphic representations of a complex semisimple Lie group G in the cohomology of certain sheaves of equivariant line bundles over the flag variety of G. The latter two theorems describe the Lie algebra cohomology of a maximal nilpotent subalgebra of Lie(G) with coefficients in an irreducible Lie(G)-module. Applications to geometry and representation theory are given. Also included is a brief overview of Schmid's far-reaching generalization of the Borel--Weil--Bott theorem to the setting of unitary representations of real semisimple Lie groups on (possibly infinite-dimensional) Hilbert spaces.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectLie groupsen
dc.subjectrepresentation theoryen
dc.subjectgeometryen
dc.titleOn the Representation Theory of Semisimple Lie Groupsen
dc.typeMaster Thesisen
dc.pendingfalseen
dc.subject.programPure Mathematicsen
uws-etd.degree.departmentPure Mathematicsen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages