Irreducible highest-weight modules and equivariant quantization

Details Irreducible highest-weight modules and equivariant quantization Irreducible highest-weight modules and equivariant quantization

2005-07-17

arxiv.org/abs/math/0507348v1

Mathematics

Quantum Algebra

Latex, 19 pages

Scientific paper

We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules $M(\lambda)$ for generic weight $\lambda$ to the case of general $\lambda$. We consider the relationship between the Shapovalov form on an irreducible highest weight module of a semisimple complex Lie algebra, fusion elements, and equivariant quantization. We also discuss some limiting properties of fusion elements. [KMST] E. Karolinsky and A. Stolin, Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization, Lett. Math. Phys., 71 (2005), p.179-197; e-print math.QA/0309203.

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