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Journal of the London Mathematical Society 1978 s2-18(1):50-60; doi:10.1112/jlms/s2-18.1.50
© 1978 by London Mathematical Society
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© Oxford University Press

Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules

A. Joseph

Centre de mathématiques Bâtiment 425, 91405 Orsay, France

Received 22 April 1977. Revision received 13 June 1977.

Let g be a complex semisimple Lie algebra, let U(g) denote the enveloping algebra of g and Prim U(g) the set of primitive ideals of U(g). Given I {euro} Prim U(g), the Gelfand-Kirillov dimension Dim U(g)/I of the quotient algebra U(g)/I is an important invariant which is useful in distinguishing elements of Prim U(g). Based on a result [12] for the principal series a new formula for Dim U(g)/I is obtained. Combined with the results of [1], [11], and [12], this gives for example the precise value of this invariant for g simple of type An. It also leads to a classification of Prim U(g) over fibres of rank 3.


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