Abstract
Formulae developed to give a positive answer to Dixmier's problem for Verma and principal series submodules are used to show that each primitive ideal in the enveloping algebra of a semisimple Lie algebra identifies with a left ideal in the group algebra of the Weyl group. The possible behaviour of these left ideals under right multiplication leads to a conjecture for the set of order relations in the primitive spectrum.
This paper was written while the author was a guest of the Institute for Advanced Studies, The Hebrew University of Jerusalem and on leave of absence from the Centre National de la Recherche Scien tifique, France. (August 1978).
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References
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Joseph, A. (1979). W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra. In: Carmona, J., Vergne, M. (eds) Non-Commutative Harmonic Analysis. Lecture Notes in Mathematics, vol 728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063341
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DOI: https://doi.org/10.1007/BFb0063341
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