Chip firing on Dynkin diagrams and McKay quivers

DOI10.1007/s00209-017-2034-5zbMath1448.17015arXiv1601.06849OpenAlexW2962676793MaRDI QIDQ667637

Caroline J. Klivans, Victor Reiner, Georgia M. Benkart

Publication date: 1 March 2019

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06849

zbMATH Keywords

root systemM-matrixDynkin diagramZ-matrixMcKay correspondencechip firingabelianizationnumbers gamesandpileavalanche-finite matrixhighest rootMcKay quiverminuscule weighttoppling

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) McKay correspondence (14E16) Root systems (17B22)

Related Items

Critical groups of group representations, Differential posets, Cayley graphs, and critical groups, Root system chip-firing, Walks on graphs and their connections with tensor invariants and centralizer algebras, Abelian networks IV. Dynamics of nonhalting networks, Tensor product Markov chains, The critical groups of Adinkras up to 2-rank of Cayley graphs, Critical groups for Hopf algebra modules, Differential posets and restriction in critical groups, Sorting via chip-firing, Enumerating linear systems on graphs, Root system chip-firing. I: Interval-firing, Eigenvalues and critical groups of Adinkras

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