Séminaire Lotharingien de Combinatoire, 91B.33 (2024), 12 pp.
Tal Gottesman
Antichains in The Representation Theory of Finite Lattices
Abstract.
The interface between the combinatorics of a partially ordered set (poset) and the representation theory of its incidence algebra has been studied for a long time. Antichains naturally arise as encoding certain representations of combinatorial nature. In this paper, we study antichains with extra properties motivated by the search for good bases for the Coxeter matrix of a poset and the hope of categorifying its properties. We then turn to a concrete example where our methods apply nicely and solve a conjecture on the poset of cominuscule roots.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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