# Dmitri Panyushev (Institute for information transmission problems of the Russian academy of sciences)

## Minimal inversion complete sets in Weyl groups and maximal abelian ideals.

Let $$\mathfrak{b}$$ be a Borel subalgebra of a simple Lie algebra $$\mathfrak{g}$$ and $$W$$ the Weyl group. In my talk, I explain a relationship between the maximal abelian ideals of $$\mathfrak{b}$$ and the minimal inversion complete sets of $$W$$. The latter have been recently defined by Malvenuto et al. (J. Algebra, 2015).