Title
Dual filtered graphs
Department/School
Mathematics
Date
9-10-2018
Document Type
Article
Abstract
We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theoretic analogues of Young's lattice, of shifted Young's lattice, and of the Young-Fibonacci lattice. We suggest notions of tableaux, insertion algorithms, and growth rules whenever such objects are not already present in the literature. We also provide a large number of other examples. Most of our examples arise via two constructions, which we call the Pieri construction and the Mobius construction. The Pieri construction is closely related to the construction of dual graded graphs from a graded Hopf algebra, as described by Bergeron-Lam-Li, Nzeutchap, and Lam-Shimizono. The Mobius construction is more mysterious but also potentially more important, as it corresponds to natural insertion algorithms.
Published in
Algebraic Combinatorics
Citation/Other Information
Patrias, R., Pylyavskyy, P. (2018). Dual filtered graphs. Algebraic Combinatorics, Volume 1(4): 441-500. https://doi.org/10.5802/alco.21.