dc.contributor.author |
Krayem, Janane Moussa |
dc.date.accessioned |
2020-03-27T22:52:15Z |
dc.date.available |
2020-03-27T22:52:15Z |
dc.date.issued |
2019 |
dc.date.submitted |
2019 |
dc.identifier.other |
b23518479 |
dc.identifier.uri |
http://hdl.handle.net/10938/21672 |
dc.description |
Thesis. M.S. American University of Beirut. Department of Mathematics, 2019. T:6981. |
dc.description |
Advisor : Dr. Kamal Khuri-Makdisi, Professor, Mathematics ; Members of Committee : Dr. Wissam Raji, Associate Professor, Mathematics ; Dr. Nicolas Mascot, Assistant Professor, Mathematics. |
dc.description |
Includes bibliographical references (leaves 77-78) |
dc.description.abstract |
Jacquet and Langlands (1970) showed that every infinite dimensional, irreducible, admissible representation of GL(2,Qp) has a unique Kirillov model, i.e. is isomorphic to a representation (π,K), where the space K consists of locally constant functions on Qp☓ on which π operates in some special way. The thesis will cover the proof of the above result after constructing the convenient framework. For this purpose I will start by introducing the notion of admissible representations of GL(2,Qp) and do some topology on Qp. After that I will prove the existence of the Kirillov model and prove some properties of the Bruhat-Schwartz space. Then I will prove the uniqueness part, which requires the construction of commutative operators; this part is the heart of the thesis. I shall then study a special example: the principal series representation. The last part of the thesis is dedicated to an application to the local new vectors of a representation. |
dc.format.extent |
1 online resource (ix, 78 leaves) : illustrations |
dc.language.iso |
eng |
dc.subject.classification |
T:006981 |
dc.subject.lcsh |
p-adic numbers. |
dc.subject.lcsh |
Number theory. |
dc.title |
Admissible representations of GL(2,Qp), the Kirillov model and application to local new vectors. |
dc.type |
Thesis |
dc.contributor.department |
Department of Mathematics |
dc.contributor.faculty |
Faculty of Arts and Sciences |
dc.contributor.institution |
American University of Beirut |