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Root systems of Levi type for Lie algebras of affine type

Behrang, Zahra (2015)
Ph.D. thesis, University of Birmingham.

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Abstract

Let g = g(\(A\)) be a Kac--Moody Lie algebra with generalized Carlan matrix \(A\). Brundan, Goodwin and independently Kostant developed a theory of root system known as Levi type root system when \(A\) is a Carlan matrix so that g(\(A\)) is a finite dimensional semisimple Lie algebra. This theory replicates much of the structure of usual root systems. In this thesis we build up the theory of Lie algebras to review this. Then we go on to define Levi type roots for the case where \(A\) is of affine type. To describe Levi type root systems we show how these roots are related to the roots of centralizers of nilpotent elements in g. We also determine the normalizers of parabolic subgroups of finite and affine Weyl groups of classical types which can be viewed as the Weyl groups for so called root systems.

Type of Work:Ph.D. thesis.
Supervisor(s):Goodwin, Simon
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:5701
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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