B-stable ideals in the nilradical of a Borel subalgebra

Eric Sommers

Published 2003-03-14, updated 2003-09-19Version 2

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 compute the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.