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

Ghatei, Davoud (2015). Spin covers of maximal compact subgroups of Kac-Moody groups and of Weyl groups. University of Birmingham. Ph.D.

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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:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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