Double quantization of $\cp$ type orbits by generalized Verma modules
arXiv:math/9803155 · doi:10.1016/S0393-0440(98)00025-4
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.
21 pages, LaTeX, no figures