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oai:digital.library.adelaide.edu.au:2440/803422016-10-21T04:34:00Zcom_2440_14759col_2440_14760

Eastwood, Michael George Sawon, Justin Dept. of Pure Mathematics 1997 http://hdl.handle.net/2440/80342 Verma modules play an important part in the theory of invariant operators on homogeneous spaces. If G is a semisimple Lie group and P a parabolic subgroup of G, then there is often a differential geometry for which the homogeneous space G/P represents the flat model. An example is conformal geometry, where G is the special orthogonal group SO(n, C). A Verma module homomorphism will corresponds to an invariant operator on the flat space. The obvious question is: how can we generalize these operators to cases where there is curvature? In this thesis we will look at a variation of Verma modules called semiholonomic Verma modules, introduced by Eastwood and Slovák. They have studied the conformal case in detail, but here we will investigate instead the exceptional case of G = E₆. We will investigate when a Verma module homomorphism lifts to a semi-holonomic Verma module homomorphism. When this happens, we can deduce that there is a curved analogue of the corresponding invariant operator. Thesis (Ph.D.) -- University of Adelaide, Dept. of Pure Mathematics, 1997 homomorphisms; semi-holonomic; Verma; modules Homomorphisms of semi-holonomic verma modules : an exceptional case. Thesis This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exception. If you are the author of this thesis and do not wish it to be made publicly available or If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legalsopen.access