Ideals of coadjoint orbits of nilpotent Lie algebras

Author:

Godfrey Colin

Abstract

For f a linear functional on a nilpotent Lie algebra g over a field of characteristic 0, let J ( f ) J(f) be the ideal of all polynomials in S ( g ) S(g) vanishing on the coadjoint orbit through f in g {g^\ast } , and let I ( f ) I(f) be the primitive ideal of Dixmier in the universal enveloping algebra U ( g ) U(g) , corresponding to the orbit. An inductive method is given for computing generators P 1 , , P r {P_1}, \ldots ,{P_r} of J ( f ) J(f) such that φ P 1 , , φ P r \varphi {P_1}, \ldots ,\varphi {P_r} generate I ( f ) , φ I(f),\varphi being the symmetrization map from S ( g ) S(g) to U ( g ) U(g) . Upper bounds are given for the number of variables in the polynomials P i {P_i} and a counterexample is produced for upper bounds proposed by Kirillov.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

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