Date of Award

8-1-2015

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Ban, Dubravka

Abstract

AN ABSTRACT OF THE DISSERTATION OF WAHIDAH ALSIBIANI, for the Doctor of Philosophy degree in MATHEMATICS, presented on MAY 27Th, 2015, at Southern Illinois University Carbondale. TITLE: REDUCIBILITY OF PARABOLICALLY INDUCED REPRESENTATIONS MAJOR PROFESSOR: Dr. D. Ban Reducibility of parabolically induced representations of $p$-adic groups is one of the basic questions in the representation theory, and generally a hard question. This paper presents how to reduced this question to determining reducibility of representations induced from maximal parabolic subgroups, which significantly simplifies the problem.

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