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

Abstract

AbstractWe give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit Oℝof SL(3,ℝ). The space of quantization is the space of holomorphic functions on 𝕔2- {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 𝕔2- {0}) (the universal cover of Oℝ) with Kaehler potential ρ |z|4.