# 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.
Supervisor(s):
Supervisor(s)EmailORCID
Gramlich, RalfUNSPECIFIEDUNSPECIFIED
Shpectorov Prof., SergeyUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/6027

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