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# $B$-Stable Ideals in the Nilradical of a Borel Subalgebra

Published:2005-09-01
Printed: Sep 2005
• Eric N. Sommers
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## Abstract

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.
 MSC Classifications: 20F55 - Reflection and Coxeter groups [See also 22E40, 51F15] 17B20 - Simple, semisimple, reductive (super)algebras 05E99 - None of the above, but in this section