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

Abstract

It is known that symmetric orbits in ${\mathbf{g}}^{\ast }$ for any simple Lie algebra $\mathbf{g}$ 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 $sl(n+1{)}^{\ast }$ whose real compact form is $C{P}^n$) by means of q-deformed Verma modules.

21 pages, LaTeX, no figures

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Double quantization on the coadjoint representation of sl(n)
• Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere

Cited by in corpus (5)

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