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Spin covers of maximal compact subgroups of Kac-Moody groups and of Weyl groups

Ghatei, Davoud (2015)
Ph.D. thesis, University of Birmingham.

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Abstract

The maximal compact subgroup SO(\(n\),ℝ) of SL(\(n\),ℝ) admits two double covers Spin (\(n\),ℝ) and O(\(n\),ℝ). In this thesis we show that in fact given any simply-laced diagram ∆, with associated split real Kac-Moody group \(G\)(∆), the 'maximal compact' subgroup \(K\)(∆)also admits a double cover Spin(∆). We then describe a subgroup of Spin(∆) which is a cover of the Weyl group \(W\)(∆) associated to g(∆). This answers a conjecture of Damour and Hillmann. Moreover, the group \(D\) which extends \(W\) is used in an attempt to classify the images of the so-called generalised spin representations.

Type of Work:Ph.D. thesis.
Supervisor(s):Gramlich, Ralf and Shpectorov, Sergey (Prof.)
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:6027
This unpublished thesis/dissertation is copyright of the author and/or third parties.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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