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Search: MSC category 22E70 ( Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10] )

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1. CJM 2001 (vol 53 pp. 278)

Helminck, G. F.; van de Leur, J. W.
Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting
In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the $\KP$ hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of $\tau$-functions is given.

Keywords:KP hierarchy, Darboux transformation, Grassmann manifold
Categories:22E65, 22E70, 35Q53, 35Q58, 58B25

2. CJM 1997 (vol 49 pp. 916)

Brylinski, Ranee
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 $\rho=|z|^4$.

Categories:81S10, 32C17, 22E70

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