Bruhat order on plane posets and applications

2012/11/23 by Foissy, Loïc
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1211.5449

Abstract

A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space H_PP generated by PP, using the notion of biideals of plane posets. We here define a partial order on PP, making it isomorphic to the set of partitions with the weak Bruhat order. We prove that this order is compatible with both products of PP; moreover, it encodes a non degenerate Hopf pairing on the infinitesimal Hopf algebra H_PP.

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