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Zbl 0762.17007
Garfinkle, Devra
On the classification of primitive ideals for complex classical Lie algebras. II. (English)
[J] Compos. Math. 81, No.3, 307-336 (1992). ISSN 0010-437X; ISSN 1570-5846/e

This paper continues the series of four papers classifying the primitive ideals in the enveloping algebra of a semisimple Lie algebra $\germ g$ of classical type. The first paper in the series [Compos. Math. 75, No. 2, 135-169 (1990; Zbl 0737.17003)] set up the basic combinatorial machine to do the classification. Given an element $w$ in the Weyl group $W$ of $\germ g$, it introduced a generalization of the classical Robinson- Schensted algorithm to produce a pair of so-called standard domino tableaux. Then it modified the first tableau in the pair to make it have ``special shape''. In view of the standard facts on inclusions of primitive ideals established by Joseph in the late 1970s, the proof that the algorithm classifies primitive ideals comes down to analyzing how the various steps in it affect the $\tau$-invariant of $w$. This paper carries out this analysis. \par The third paper in the series then completes the classification in types $B$ and $C$ (type $A$ being already known), while the fourth paper will treat type $D$.
[W.M.McGovern (Seattle)]

MSC 2000:: *17B35 Universal enveloping algebras (Lie algebras)
17B10 Representations of Lie algebras, algebraic theory
22E47 Repres. of Lie and real algebraic groups: algebraic methods

Keywords: enveloping algebra; semisimple Lie algebra; Robinson-Schensted algorithm; primitive ideals; domino tableaux; special shape; $\tau$-invariant

Citations: Zbl 0737.17003

Cited in: Zbl 0798.17007

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