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A note on primitive ideals and characteristic classes. (English) Zbl 0576.17007

Geometry today, Int. Conf., Rome 1984, Prog. Math. 60, 11-20 (1985).
[For the entire collection see Zbl 0563.00006.]
The authors’ summary: ”To a primitive ideal in the enveloping algebra of a semisimple Lie algebra, we associate a certain cohomology class on the flag variety, which turns out to be essentially Joseph’s Goldie rank polynomial. Moreover we express the latter in terms of Chern and Segre classes of certain cone bundles related to nilpotent conjugacy classes. Our objects are to gain insight into the geometry of nilpotent varieties, the classification of primitive ideals, and the relation between them.”

MSC:

17B35 Universal enveloping (super)algebras
14L30 Group actions on varieties or schemes (quotients)

Citations:

Zbl 0563.00006