On orbits of antichains of positive roots

2007/11/21 by Dmitri I. Panyushev, Panyushev, Dmitri I. · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.0711.3353

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

openalex publication_date 2007/11/21 · arxiv created 2008/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Δ⁺ is the set of positive roots and Π is the set of simple roots in Δ⁺, then we consider the cases P=Δ⁺ and Δ⁺∖ Π. For the root system of type A_n, we consider an X-invariant integer-valued function on the set of antichains of Δ⁺ and establish some properties of it.

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