Eriksson's numbers game and finite Coxeter groups

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Eriksson's numbers game and finite Coxeter groups
The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. This game and its interactions with Coxeter/Weyl group theory and Lie theory have been studied by many authors. In particular, Eriksson connects certain geometric representations of Coxeter groups with games on graphs with certain real number amplitudes. Games played on such graphs are "E-games." Here we investigate various finiteness aspects of E-game play: We extend Eriksson's work relating moves of the game to reduced decompositions of elements of a Coxeter group naturally associated to the game graph. We use Stembridge's theory of fully commutative Coxeter group elements to classify what we call here the "adjacency-free" initial positions for finite E-games. ...
Robert G. Donnelly
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where EJC
Authors Robert G. Donnelly
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