Abstract. In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the C∗-algebra ON . A main tool in our analysis is the infinite-dimensional group of all maps T → U (N) (where U (N) is the group of all unitary N-by-N ma...

Let X be a geodesic space and G a group acting geometrically on X. A discrete halfspace system of X is a set H of open halfspaces closed under h 7→ X r h and such that every x ∈ X has a neighbourhood intersecting only finitely many walls of H. Given such a system H, one uses the Sageev-Roller construction to form a cubing C(H). When H is invariant under G we have: Theorem A. X has a G-equivaria...

Building upon earlier work of T. Brady, we construct locally CAT(0) classifying spaces for those Artin groups which are three dimensional and which satisfy the FC (flag complex) condition. The approach is to verify the “link condition” by applying gluing arguments for CAT(1) spaces and by using the curvature testing techniques of M. Elder and J. McCammond.

The construction of the fusion ring of a quasi-rational CFT based on sl(3) k at generic level k ∈ Q is reviewed. It is a commutative ring generated by formal characters, elements in the group ring Z[ ˜ W ] of the extended affine Weyl group˜W of sl(3) k. Some partial results towards the sl(4) k generalisation of this character ring are presented.

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska [18]. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper is the first in a series. In...

Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbers. The same holds for a Sylow 2-subgroup of C.

We show that any finitely generated Coxeter group acts properly discontinuously on a locally finite, finite dimensional CAT(0) cube complex. For any word hyperbolic or right angled Coxeter group we prove that the cubing is cocompact. We show how the local structure of the cubing is related to the partial order studied by Brink and Howlett in their proof of automaticity for Coxeter groups. In hi...