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COMPOSITION FACTORS OF QUOTIENTS OF THE UNIVERSAL ENVELOPING ALGEBRA BY PRIMITIVE IDEALS

Published online by Cambridge University Press:  03 December 2004

CATHARINA STROPPEL
CATHARINA STROPPEL
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United [email protected]
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Abstract

Graded versions of the principal series modules of the category $\cO$ of a semisimple complex Lie algebra $\mg$ are defined. Their combinatorial descriptions are given by some Kazhdan–Lusztig polynomials. A graded version of the Duflo–Zhelobenko four-term exact sequence is proved. This gives results about composition factors of quotients of the universal enveloping algebra of $\mg$ by primitive ideals; in particular an upper bound is obtained for the multiplicities of such composition factors. Explicit descriptions are given of principal series modules for Lie algebras of rank $2$. It can be seen that these graded versions of principal series representations are neither rigid nor Koszul modules.

Keywords

17B1017B3522E46
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 643 - 658
Copyright
The London Mathematical Society 2004

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Footnotes

This work was partially supported by the EEC program ERB FMRX-CT97-0100.