P. Tukia published in T2] the rst example of a uniformly quasi-isometric and hence quasiconformal group acting on R n , n 3, which is not a quasiconformal conjugate of any MM obius group. We have analyzed this group and have shown that it contains elements which generate cyclic parabolic uniformly quasi-isometric groups that cannot be conjugated by a quasi-conformal map to a MM obius group. By ...

We provide two algorithms to solve branching from K to M for the real split reductive group of type An, one inductive and one related to semistandard Young tableaux. The results extend to branching from Ke to M fnl Ke for the real split reductive groups of type Bn and Dn. Thesis Supervisor: David A. Vogan, Jr. Title: Professor of Mathematics

With each piecewise monotonic map τ of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t −1 ] module , is finitely generated, and generators are identified. Dimension groups are computed for Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is shown that the dimension group defined here is isomor-phic to K 0 (A), where A is a...

We study the moduli space of vacua of four dimensional N = 1 and N = 2 supersymmetric gauge theories with the gauge groups Sp(2Nc), SO(2Nc) and SO(2Nc + 1) using the M theory fivebrane. Higgs branches of the N = 2 supersymmetric gauge theories are interpreted in terms of the M theory fivebrane and the type IIA s-rule is realized in it. In particular we construct the fivebrane configuration whic...

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity function m on its root system is defined as the joint kernel of the properly gauged invariant integrals of the corresponding generalised quantum Calogero-Moser problem. The relation between this space and the ring of all quantum integrals of this system (which is isomorphic to the ring of corresponding quasiinva...

Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group Z, whose square is not Mengerbounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and Sanchis.

Assume p∗ is a meager type in a superstable theory T . We investigate definability properties of p∗-closure. We prove that if T has < 2א0 countable models then the multiplicity rank M of every type p is finite. We improve Saffe’s conjecture. 0. Introduction. Throughout the paper, T is a superstable theory in a countable language L, and we work within a monster model C = C of T . The general ref...