On the Representation Theory of Semisimple Lie Groups
dc.contributor.author | Al-Faisal, Faisal | |
dc.date.accessioned | 2010-08-30T20:45:26Z | |
dc.date.available | 2010-08-30T20:45:26Z | |
dc.date.issued | 2010-08-30T20:45:26Z | |
dc.date.submitted | 2010 | |
dc.description.abstract | This 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.identifier.uri | http://hdl.handle.net/10012/5421 | |
dc.language.iso | en | en |
dc.pending | false | en |
dc.publisher | University of Waterloo | en |
dc.subject | Lie groups | en |
dc.subject | representation theory | en |
dc.subject | geometry | en |
dc.subject.program | Pure Mathematics | en |
dc.title | On the Representation Theory of Semisimple Lie Groups | en |
dc.type | Master Thesis | en |
uws-etd.degree | Master of Mathematics | en |
uws-etd.degree.department | Pure Mathematics | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |
uws.typeOfResource | Text | en |