1,869 research outputs found
The isomorphism problem for Coxeter groups
By a recent result obtained by R. Howlett and the author considerable
progress has been made towards a complete solution of the isomorphism problem
for Coxeter groups. In this paper we give a survey on the isomorphism problem
and explain in particular how the result mentioned above reduces it to its
`reflection preserving' version. Furthermore we desrcibe recent developments
concerning the solution of the latter.Comment: 15 pages, 0 figures, to appear in 'The Coxeter Legacy: Reflections
and Projections', Fields Institute Communication
Twist-rigid Coxeter groups
We prove that two angle-compatible Coxeter generating sets of a given
finitely generated Coxeter group are conjugate provided one of them does not
admit any elementary twist. This confirms a basic case of a general conjecture
which describes a potential solution to the isomorphism problem for Coxeter
groups.Comment: 28 pages, 1 figur
Cuspidal Calogero-Moser and Lusztig families for Coxeter groups
The goal of this paper is to compute the cuspidal Calogero–Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the symplectic leaves of the associated Calogero–Moser space and then by classifying certain “rigid” modules. Numerical evidence suggests that there is a very close relationship between Calogero–Moser families and Lusztig families. Our classification shows that, additionally, the cuspidal Calogero–Moser families equal cuspidal Lusztig families for the infinite families of Coxeter groups
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