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dc.contributor.authorAl-Faisal, Faisal 20:45:26 (GMT) 20:45:26 (GMT)
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.publisherUniversity of Waterlooen
dc.subjectLie groupsen
dc.subjectrepresentation theoryen
dc.titleOn the Representation Theory of Semisimple Lie Groupsen
dc.typeMaster Thesisen
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

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