Abstract
We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of Q ̌ /(h+1) Q ̌ under the Weyl group ( Q ̌ being the coroot lattice and h the Coxeter number of g ). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals.
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