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math.RT2008
Coxeter Elements and Root Bases
Alexander Kirillov, Jaimal Thind
Let g be a Lie algebra of type A,D,E with fixed Cartan subalgebra h, root system R and Weyl group W. We show that a choice of Coxeter element C gives a root basis for g. Moreover w…
math.RT2007
Coxeter Elements and Periodic Auslander-Reiten Quiver
Alexander Kirillov, Jaimal Thind
In this paper we show that for a simply-laced root system a choice of gives rise to a natural construction of the Dynkin diagram, in which vertices of the diagram correspond to…
math.RT2005★ 4 cited
Compact groups and their representations
Alexandre Kirillov, Alexander Kirillov
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.