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KÄHLER STRUCTURES AND WEIGHTED ACTIONS ON THE COMPLEX TORUS

Published online by Cambridge University Press:  01 June 2000

MENG-KIAT CHUAH
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan; [email protected]
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Abstract

Let T be the compact real torus, and TC its complexification. Fix an integral weight α, and consider the α-weighted T-action on TC. If ω is a T-invariant Kähler form on TC, it corresponds to a pre-quantum line bundle L over TC. Let Hω be the square-integrable holomorphic sections of L. The weighted T-action lifts to a unitary T-representation on the Hilbert space Hω, and the multiplicity of its irreducible sub-representations is considered. It is shown that this is controlled by the image of the moment map, as well as the principle that ‘quantization commutes with reduction’.

Type
Research Article
Copyright
The London Mathematical Society 2000

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