 00504 Brian C. Hall
 Geometric quantization and the generalized SegalBargmann transform
for Lie groups of compact type
(117K, Latex)
Dec 19, 00

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Abstract. Let K be a connected Lie group of compact type and let T*(K) be its
cotangent bundle. This paper considers geometric quantization of
T*(K) first using the vertical polarization and then using a natural
Kahler polarization obtained by identifying T*(K) with the
complexified group K_C. The first main result is that the Hilbert
space obtained by using the Kahler polarization is naturally
identifiable with the generalized SegalBargmann space introduced by
the author from a different point of view, namely that of heat kernels.
The second main result is that the pairing map of geometric
quantization coincides with the generalized SegalBargmann transform
introduced by the author. This means that in this case the pairing map
is a constant multiple of a unitary map. For both results it is
essential that the halfform correction be included when using the
Kahler polarization. Together with results of the author with
B. Driver, these results may be seen as an instance of "quantization
commuting with reduction."
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