Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for Lφ affine surface areas are established. 2000 AMS subject classification: Primary 52A20; Secondary 53A15. Finding the right notion of affine surface area was one of the first questions asked within affine differential geometry. At ...

Recently there has been much interest in Gowers uniformity norms from the perspective of theoretical computer science. This is mainly due to the fact that these norms provide a method for testing whether the maximum correlation of a function f : F p → Fp with polynomials of degree at most d ≤ p is non-negligible, while making only a constant number of queries to the function. This is an instanc...

0. Introduction 5 0.1. Objectives and main results 5 0.1.1. Affine Satake isomorphisms 5 0.1.2. Whittaker functions 6 0.1.3. The setting of the paper 7 0.2. Dunkl operators via DAHA 7 0.2.1. Families of Dunkl operators 8 0.3. The technique of spinors 9 0.3.1. Connections to AKZ 9 0.3.2. Isomorphism theorems 10 0.3.3. The localization functor 10 0.3.4. The Whittaker limit 11 0.4. On Langlands’ p...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...