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Gelfand‐Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules
Author(s) -
Joseph A.
Publication year - 1978
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-18.1.50
Subject(s) - mathematics , quotient , pure mathematics , lie algebra , invariant (physics) , rank (graph theory) , dimension (graph theory) , algebra over a field , combinatorics , mathematical physics
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 € 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 A n . It also leads to a classification of Prim U ( g ) over fibres of rank 3.