Quantum coadjoint orbits of GL(n) and generalized Verma modules

Details Quantum coadjoint orbits of GL(n) and generalized Verma modules Quantum coadjoint orbits of GL(n) and generalized Verma modules

2002-12-23

arxiv.org/abs/math/0212318v1

Mathematics

Quantum Algebra

21 pages, AMS LaTeX

Scientific paper

In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms of a generalized Verma module. As a corollary, we obtain an explicit description of the annihilators of generalized Verma modules over U(gl(n)). As an application, we construct real forms of the quantum orbits and classify finite dimensional representations. We compute the non-commutative Connes index for basic homogenous vector bundles over the quantum orbits.

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