We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic nspace, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamat...

Abstract We study cells with respect to the p -canonical basis of Hecke algebra a crystallographic Coxeter system (see Jensen and Williamson (2017) (2020)) their compatibility standard parabolic subgroups. show that after induction surrounding bigger group cell module right -cell in subgroup decomposes as direct sum modules. Along way, we state some new positivity properties basis.

We study the action of a relatively hyperbolic group on its boundary, by methods of symbolic dynamics. Under a condition on the parabolic subgroups, we show that this dynamical system is finitely presented. We give examples where this condition is satisfied, including geometrically finite kleinian groups. Associated to any word-hyperbolic group Γ, there is a dynamical system arising from the ac...

Suppose G is a semisimple Lie group with infinite center. As in the finite center case, the tempered spectrum of G consists of families of representations induced from cuspidal parabolic subgroups P = MAN. However, in the infinite center case, the representations of M to be induced are not discrete series, but are relative discrete series which occur in continuous families. In two previous pape...

2 Stabilisers of Parabolic Centralisers 6 2.1 Stabiliser Subgroups . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Generators for the Stabiliser of L . . . . . . . . . . . . . . . . 7 2.3 Ordering L and the stabiliser of L-maximal elements . . . . . 9 2.4 Ordering X and closures of elements . . . . . . . . . . . . . . 10 2.5 A matrix representation of St(L) . . . . . . . . . . . . . . . . 1...

We study general properties of the restriction of the representations of the finite complex reflection groupes G(de, e, r + 1) to their maximal parabolic subgroups of type G(de, e, r), and focus notably on the multiplicity of components. In combinatorial terms, this amounts to the following question : which symmetries arise or disappear when one changes (exactly) one pearl in a combinatorial ne...

We present algorithms for constructing explicit matrices for every irreducible representation of a Weyl group, with particular emphasis on the exceptional groups. The algorithms we present will produce representing matrices in either of two forms: real orthogonal, with matrix entries that are square roots of rationals, or rational and seminormal. In both cases, the matrices are “hereditary” in ...