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Quantization of the $4$-dimensional nilpotent orbit of $\SL(3,\R)$ |
Canad. J. Math. 49(1997), 916-943
Published:1997-10-01
Printed: Oct 1997
Printed: Oct 1997
- Ranee Brylinski
Abstract
We give a new geometric model for the quantization
of the 4-dimensional conical (nilpotent) adjoint orbit $\OR$
of $\SL(3,\R)$. The space of quantization is the space of
holomorphic functions on ${\C}^2-\{0\})$ which are square integrable
with respect to a signed measure defined by a Meijer $G$-function.
We construct the quantization out a non-flat Kaehler structure on
${\C}^2-\{0\})$ (the universal cover of $\OR$) with Kaehler potential
$\rho=|z|^4$.
| MSC Classifications: |
81S10 - Geometry and quantization, symplectic methods [See also 53D50] 32C17 - unknown classification 32C17 22E70 - Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10] |