Introduction to the quantization of orbital varieties (Q2780958)

It has been established by Kirillov that there is a bijection between the unitary representations and the co-adjoint orbits of a nilpotent Lie algebra. For other groups, in particular in the semisimple case, the orbit method consists of finding a similar relationship. This article provides an introduction to the quantization problem of orbital varieties. A set of conjectures proposed by Joseph and related results are discussed, including the papers [C. R. Acad. Sci., Paris, Sér. I 315, 537-540 (1992; Zbl 0783.22006)] and [Bull. Sci. Math., II. Sér. 118, 225-243 (1994; Zbl 0820.17005)] by the first author.