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Title: The Dirac operator on certain homogeneous spaces and representations of some Lie groups
Author: Slebarski, Stephen
ISNI:       0000 0001 3417 1084
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1983
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Let G be a real non-compact reductive Lie group and L a compact subgroup. Take a maximal compact subgroup K of G containing L, and suppose that G/L is Riemannian via a bi-invariant metric and that there is a spin structure. Then there is the Dirac operator D over G/L, on spinors with values in a unitary vector bundle. D is a first order, G-invariant, elliptic, essentially self-adjoint differential operator. It has been shown by R. Parthasarathy that with G semi-simple, rank K = rank G, 'discrete-series' representations of G can be realized geometrically on, the kernel of D (i.e. the L2-solutions of Df = 0). Following this, we are interested in how the kernel of D decomposes into irreducible representations of G, when L is any compact subgroup. In future work we expect to reduce this problem to the compact case i.e. to considering the Dirac operator on K/L. Therefore, in this Thesis, we consider the Dirac operator on a compact, Riemannian, spin homogeneous space K/L. And determine the decomposition of the kernel into irreducible representations of K. We consider the tensor product of an induced representation and a finite-dimensional representation, and apply 'inducing in stages' to the Dirac operator.
Supervisor: Not available Sponsor: Science and Engineering Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics