# B-stable ideals in the nilradical of a Borel subalgebra

This is the pre-published version harvested from ArXiv. The published version is located at http://www.ams.org/mathscinet-getitem?mr=2154088

#### Abstract

Let \$G\$G be a connected simple algebraic group over the complex numbers and \$B\$B a Borel subgroup. Let \$\germ g\$g be the Lie algebra of \$G\$G and \$\germ b\$b the Lie algebra of \$B\$B . A subspace of the nilradical of \$\germ b\$b which is stable under the action of \$B\$B is called a \$B\$B -stable ideal of the nilradical. It is called strictly positive if it intersects the simple root spaces trivially.
The author counts the number of strictly positive \$B\$B -stable ideals in the nilradical of a Borel subalgebra and proves that the set of minimal roots of any \$B\$B -stable ideal is conjugate by an element of the Weyl group to a subset of simple roots. He also counts the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.

#### Suggested Citation

EN Sommers. "B-stable ideals in the nilradical of a Borel subalgebra" Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 48.3 (2005): 460-472.
Available at: http://works.bepress.com/eric_sommers/6

﻿