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B-Stable Ideals in the Nilradical of a Borel Subalgebra

Published online by Cambridge University Press:  20 November 2018

Eric N. Sommers
Eric N. Sommers*
Affiliation:
University of Massachusetts—Amherst, Amherst, MA 01003, Institute for Advanced Study, Princeton, NJ 08540 e-mail: esommers@math.umass.edu
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Abstract

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We count the number of strictly positive $B$-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any $B$-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.

Keywords

20F5517B2005E99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 460 - 472
Copyright
Copyright © Canadian Mathematical Society 2005

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