Browsing by Author "Chuah, Meng-Kiat"

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Geometric quantization and Zuckerman models of semisimple Lie groups
(2007)
Chuah, Meng-Kiat
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應用數學系
;
Department of Applied Mathematics
Let G be a real semisimple Lie group. We equip invariant presymplectic forms omega to some fibration X over the flag domain of G. By applying geometric quantization to (X, omega), we obtain a unitary G-representation H whose subrepresentations are infinitesimally equivalent to the Zuckerman modules. The occurence of the Zuckerman modules H are controlled by the image of the moment map of omega. This leads to our notion of Zuckerman model.
The direct integral of some weighted Bergman spaces
(2007-02-01)
Chuah, Meng-Kiat
;
應用數學系
;
Department of Applied Mathematics
Let G be the abelian Lie group R(n) x R(k)/Z(k), acting on the complex space X = R(n+k) x iG. Let F be a strictly convex function on R(n+k). Let H be the Bergman space of holomorphic functions on X which are square-integrable with respect to the weight e(-F). The G-action on X leads to a unitary G-representation on the Hilbert space H. We study the irreducible representations which occur in H by means of their direct integral. This problem is motivated by geometric quantization, which associates unitary representations with invariant Kahler forms. As an application, we construct a model in the sense that every irreducible G-representation occurs exactly once in H.