On orbits of antichains of positive roots

Details On orbits of antichains of positive roots On orbits of antichains of positive roots

2007-11-21

arxiv.org/abs/0711.3353v2

Mathematics

Combinatorics

12 pages, final version; to appear in Europ. J. Combinatorics

Scientific paper

For any finite poset P, there is a natural operator $X$ acting on the antichains of P. We discuss conjectural properties of this operator for some graded posets associated with irreducible root systems. In particular, if $\Delta^+$ is the set of positive roots and $\Pi$ is the set of simple roots in $\Delta^+$, then we consider the cases $P=\Delta^+$ and $\Delta^+\setminus \Pi$. For the root system of type $A_n$, we consider an $X$-invariant integer-valued function on the set of antichains of $\Delta^+$ and establish some properties of it.

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