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Quantization of the 4-Dimensional Nilpotent Orbit of Sl(3, ℝ)

Published online by Cambridge University Press:  20 November 2018

Ranee Brylinski
Ranee Brylinski*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA, email: rkb@math.psu.edu
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Abstract

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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 ρ |z|4.

Keywords

81S1032C1722E70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 5 , 01 October 1997 , pp. 916 - 943
Copyright
Copyright © Canadian Mathematical Society 1997

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