Irreducible highest-weight modules and equivariant quantization

الأصل · EN

We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules M(λ) for generic weight λ to the case of general λ. 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.