B-stable ideals in the nilradical of a Borel subalgebra

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

2003-03-14

arxiv.org/abs/math/0303182v2

Mathematics

Representation Theory

We correct the lemmas in Section 3 in the earlier version

Scientific paper

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.

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