Timeline for Is there any need to study Coxeter systems (W,S) with S infinite?
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| Aug 22, 2013 at 17:27 | comment | added | Jim Humphreys | P.S. Concerning the citations, it may be instructive to follow them up on MathSciNet (though administrators only look at the numbers). Infinite rank probably doesn't matter so much, but the characterization of reflection subgroups as Coxeter groups is clearly important in the study of Coxeter groups for their own sake. I'm less certain about how the Dyer/Deodhar theorems interact with other subjects such as Kac-Moody theory | |
| Aug 22, 2013 at 17:26 | comment | added | Jim Humphreys | Thanks for calling attention to this natural class of examples, which I had lost track of. In an infinite irreducible (but not affine) Coxeter group, there will be some reflection subgroups of infinite rank, due to the weird "geometry" of hyperplanes and roots coming from the Coxeter matrix. Your example of the universal group of rank 3 was analyzed in early work by Dyer, for example. These are certainly "significant" examples but I guess understood in detail only from properties of their finite Coxeter subgroups. | |
| Aug 21, 2013 at 18:10 | history | edited | Andreas Blass | CC BY-SA 3.0 |
added a comma, to avoid what looked like an infinite product
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| Aug 21, 2013 at 16:14 | history | edited | David E Speyer | CC BY-SA 3.0 |
deleted 1 characters in body
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| Aug 20, 2013 at 20:17 | history | answered | David E Speyer | CC BY-SA 3.0 |