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ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  01 February 2009

JONATHAN BROWN  and
JONATHAN BRUNDAN
JONATHAN BROWN
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (email: jbrown8@uoregon.edu)
JONATHAN BRUNDAN*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (email: brundan@uoregon.edu)
*
✉For correspondence; e-mail: brundan@uoregon.edu
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Abstract

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We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

Keywords

nilpotent matricescentralizerssymmetric invariants

MSC classification

Secondary: 17B35: Universal enveloping (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 1 - 15
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

Research supported in part by NSF grant no. DMS-0139019.

References

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