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Equivalence Classes of Ideals in the Nilradical of a Borel Subalgebra

Published online by Cambridge University Press:  11 January 2016

Eric N. Sommers
Eric N. Sommers*
Affiliation:
University of Massachusetts—Amherst Amherst, MA 01003 U.S.A. esommers@math.umass.edu
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Abstract

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An equivalence relation is defined and studied on the set of B-stable ideals in the nilradical of the Lie algebra of a Borel subgroup B. Techniques are developed to compute the equivalence relation and these are carried out in the exceptional groups. There is a natural partial order on equivalence classes coming from inclusion of one ideal in another. A main theorem is that this partial order is a refinement of the closure ordering on nilpotent orbits.

Keywords

17B2020F55

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 183 , 2006 , pp. 161 - 185
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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