We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The standard constructions of subarrangements and restrictions, which are known in the case of finite hyperplane arrangements, work as well in this more general setting.
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Michael Cuntz, Bernhard Mühlherr, Christian J. Weigel, Simplicial arrangements on convex cones. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 147–191DOI 10.4171/RSMUP/138-8