Parahoric projection for twin trees

Abstract

Geometrical configurations (for example, of points and lines in a plane) have been studied for a long time. The simplest configurations are often rigid, and so we search for more interesting ones. Calderbank and Noppakaew [16] introduced the idea of parabolic projection in order to obtain new geometrical configurations from spherical buildings. Roughly speaking, a building, introduced by Tits [41] is a chamber system with some added constraints. There are three types of buildings: spherical, affine and indefinite.

The motivation for this thesis is to start developing a theory of parahoric projection, the analogue of parabolic projection, but for the case of affine buildings since it is the next natural step after the spherical case.

In the finite parabolic projection one key ingredient is the notion of oppositeness since the idea is to project so-called weakly opposite apartments. In this thesis, we define the analogue of this in the affine case using the notion of twin buildings, and we show that under some constraints these weakly opposite apartments exist and that the lifting problem has a solution in the case of A1.

Date of Award	22 Feb 2018
Original language	English
Awarding Institution	University of Bath
Supervisor	David Calderbank (Supervisor) & Gunnar Traustason (Supervisor)