Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials.
Buildings and non-positively curved polygons of finite groups.
Cambrian fans
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...
Cells and constructible representations in type .
Choosing roots of polynomials with symmetries smoothly.
Climbing elements in finite Coxeter groups.
Cohomology rings of spaces of generic bipolynomials and extended affine Weyl groups of serie
A bipolynomial is a holomorphic mapping of a sphere onto a sphere such that some point on the target sphere has exactly two preimages. The topological invariants of spaces of bipolynomials without multiple roots are connected with characteristic classes of rational functions with two poles and generalized braid groups associated to extended affine Weyl groups of the serie . We prove that the cohomology rings of the spaces of bipolynomials of bidegree stabilize as tends to infinity and that...
Coloured generalised Young diagrams for affine Weyl-Coxeter groups.
Commensurability of graph products.
Compact hyperbolic Coxeter -polytopes with facets.
Complete presentations of Coxeter groups.
Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup
Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces.
Computation in Coxeter groups. I: Multiplication.
Computing Kazhdan-Lusztig polynomials for arbitrary Coxeter groups.
Conjugacy of Coxeter elements.
Constructing irreducible representations of Weyl groups.
Coxeter classes of unitary reflection groups.
Coxeter group actions on the complement of hyperplanes and special involutions
We consider both standard and twisted actions of a (real) Coxeter group on the complement to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in and give explicit formulae which describe both actions on the total cohomology in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group , the Weyl groups...
Coxeter groups, Salem numbers and the Hilbert metric