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Title: Regular representations of GLₙ(O) and the inertial Langlands correspondence
Author: Szumowicz, Anna Maria
ISNI:       0000 0004 8501 6254
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2019
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This thesis is divided into two parts. The first one comes from the representation theory of reductive p-adic groups. The main motivation behind this part of the thesis is to find new explicit information and invariants of the types in general linear groups. Let F be a non-Archimedean local field and let O_F be its ring of integers. We give an explicit description of cuspidal types on p(O_F), with p prime, in terms of orbits. We determine which of them are regular representations and we provide an example which shows that an orbit of a representation does not always determine whether it is a cuspidal type or not. At the same time we prove that a cuspidal type for a representation π of GL_p(F) is regular if and only if the normalised level of π is equal to m or m - 1/p for m ΣZ. The second part of the thesis comes from the theory of integer-valued polynomials and simultaneous p-orderings. This is a joint work with Mikołaj Frączyk. The notion of simultaneous p-ordering was introduced by Bhargava in his early work on integer-valued polynomials. Let k be a number field and let O_k be its ring of integers. Roughly speaking a simultaneous p-ordering is a sequence of elements from O_k which is equidistributed modulo every power of every prime ideal in O_k as well as possible. Bhargava asked which subsets of Dedekind domains admit simultaneous p-ordering. Together with Mikołaj Frączyk we proved that the only number field k with O_k admitting a simultaneous p-ordering is Q.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available