LIFTING OF CHARACTERS AND FUNCTIONS ON METAPLECTIC GROUPS
| dc.contributor.advisor | ADAMS, JEFFREY D | en_US |
| dc.contributor.author | Trehan, Amit | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2005-02-02T06:35:28Z | |
| dc.date.available | 2005-02-02T06:35:28Z | |
| dc.date.issued | 2004-11-23 | en_US |
| dc.description.abstract | We study the lifting of representations between the N-fold metaplectic covers of SL(n, F) where n|N and PGL(n, F), F a local field, and obtain a formula relating irreducible characters of PGL(n, F) and SL~(n, F) (the covers of SL(n, F)). This is achieved by generalizing the approach of Adams [1]. In the second part of the thesis we study the lifting of functions between SL~(n, F) and PGL(n, F). Using orbital integrals we obtain the formula for the lifting of characters as a dual to the lifting of functions. This is based on the methods of Flicker and Kazhdan [7]. Finally we use our methods of lifting of orbital integrals to provide alternate proof of a well-known fact about p-adic fields (under certain restrictions). We show that for a Galois extension E/F, F*/N(E*) isomorphic Gal(E/F)ab where Gal(E/F) is the Galois group of E over F and Gal(E/F)ab denotes its abelianization and N: E* to F* is the norm map. | en_US |
| dc.format.extent | 406335 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/2048 | |
| dc.language.iso | en_US | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | REPRESENTATIONS | en_US |
| dc.subject.pquncontrolled | ORBITAL INTEGRALS | en_US |
| dc.subject.pquncontrolled | LOCAL FIELDS | en_US |
| dc.title | LIFTING OF CHARACTERS AND FUNCTIONS ON METAPLECTIC GROUPS | en_US |
| dc.type | Dissertation | en_US |
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