Invariant convex subcones of the Tits cone of a linear Coxeter group

2015/11/18 by Claus Mokler, Mokler, Claus
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1511.05899

65 pages, slightly extended and final version, to appear in the Journal of Pure and Applied Algebra

arxiv created 2017/09/12 · arxiv updated 2017/09/13

Abstract

We investigate the faces and the face lattices of arbitrary Coxeter group invariant convex subcones of the Tits cone of a linear Coxeter system as introduced by E. B. Vinberg. Particular examples are given by certain Weyl group invariant convex cones which underlie the theory of normal reductive linear algebraic monoids as developed by M. S. Putcha and L. E. Renner. We determine the faces and the face lattice of the Tits cone and the imaginary cone, generalizing some of the results obtained for linear Coxeter systems with symmetric root bases by M. Dyer, and for linear Coxeter systems with free root bases by E. Looijenga, P. Slodowy, and the author.

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