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Abstract view

# Quantization of the $4$-dimensional nilpotent orbit of SL(3,$\mathbb{R}$)

We give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit $O_\mathbb{R}$ of SL$(3,\mathbb{R})$. The space of quantization is the space of holomorphic functions on $\mathbb{C}^2- \{ 0 \}$ 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 $\mathbb{C}^2 - \{ 0 \}$ (the universal cover of $O_\mathbb{R}$ ) with Kaehler potential $\rho=|z|^4$.