Akiyoshi Tsuchiya: Two enriched poset polytopes

Abstract: Richard Stanley introduced two lattice polytopes associated to a finite partially ordered set (poset for short), which are called the order polytope and the chain polytope. These polytopes are of interest in combinatorics, commutative algebra, algebraic geometry and representation theory. In particular, these polytopes are related to the theory of P-partitions. In this talk, we introduce two lattice polytopes associated to a finite poset, which are called the enriched order polytope and the enriched chain polytope, from a viewpoint of the theory of (left) enriched P-partitions which were introduced by John Stembridge. In particular, we show algebraic and combinatorial properties of these polytopes. This talk is based on joint work with Hidefumi Ohsugi.