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Double quantization of $\cp$ type orbits by generalized Verma modules

J. Donin·D. Gurevich·S. Khoroshkin
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Abstract

It is known that symmetric orbits in ${\bf g}^*$ for any simple Lie algebra ${\bf g}$ are equiped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the "canonical" R-matrix. We realize quantization of this Poisson pencil on $\cp$ type orbits (i.e. orbits in $sl(n+1)^*$ whose real compact form is $ CP^n$) by means of q-deformed Verma modules.

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J. Donin, D. Gurevich, S. Khoroshkin. 1998-03-31. Double quantization of $\cp$ type orbits by generalized Verma modules. https://doi.org/10.1016/s0393-0440(98)00025-4

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