| Publication Type |
dissertation |
| School or College |
College of Science |
| Department |
Mathematics |
| Author |
Kitchen, Sarah Noelle |
| Title |
Localization of cohomologically induced modules to partial flag varieties |
| Date |
2010-05 |
| Description |
Cohomological induction gives an algebraic method for constructing representations for a real reductive Lie group G from irreducible representations of reductive subgroups. Beilinson-Bernstein Localization alternatively gives a geometric method for constructing Harish-Chandra modules for G, with a fixed infinitessimal character, from some specific representations of a Cartan subgroup which depend on the character. The duality theorem of Hecht, Milicic, Schmid and Wolf establishes a relationship between modules cohomologically induced from a Cartan and the sheaf cohomology of the D-modules on the complex flag variety for G determined by the Beilinson-Berstein construction. The main results of this thesis give a generalization of the duality theorem to partial flag varieties, which recovers cohomologically induced modules arising from larger reductive subgroups. |
| Type |
Text |
| Publisher |
University of Utah |
| Subject |
Localization; Cohomologically induced modules; Partial flag varieties; Cohomological induction; Lie groups |
| Subject LCSH |
Cohomology operations; Modules (Algebra) |
| Dissertation Institution |
University of Utah |
| Dissertation Name |
PhD |
| Language |
eng |
| Rights Management |
©Sarah Noelle Kitchen |
| Format Medium |
application/pdf |
| Format Extent |
582,562 bytes |
| Identifier |
us-etd2,152617 |
| Source |
Original in Marriott Library Special Collections, QA3.5 2010 .K58 |
| ARK |
ark:/87278/s6xw50d4 |
| Setname |
ir_etd |
| ID |
193284 |
| Reference URL |
https://collections.lib.utah.edu/ark:/87278/s6xw50d4 |
