Completely splittable representations of symmetric groups and affine Hecke algebras

Completely Splittable Representations of Symmetric Groups

Calibrated representations of affine Hecke algebras

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated representations are indexed by placed skew shapes, (2) the dimension of an irreducible calibrated representation is the number of standard Young tableaux correspo...

Representations of rank two affine Hecke algebras

This paper classifies and constructs explicitly all the irreducible representations of affine Hecke algebras of rank two root systems. The methods used to obtain this classification are primarily combinatorial and are, for the most part, an application of the methods used in [Ra1]. I have made special effort to describe how the classification here relates to the classifications by Langlands par...

Affine Braid Groups and Hecke Algebras

These are notes for a class on double affine Hecke algebras and Macdonald polynomials given in the Fall of 2007 at the University of Minnesota. Here we introduce the (single and double) affine braid groups and Hecke algebras. We are following chapters 3,4, and 5 of Macdonald’s book [Mac]. There is also an (optional) aside giving applications to the T -equivariant K-theory of flag varieties G/B....

Analytic R-groups of Affine Hecke Algebras

Date: September 7, 2009. 2000 Mathematics Subject Classification. Primary 20C08; Secondary 22D25, 22E35, 43A30. During the preparation of this paper the first named author was supported by the program ANR-08-BLAN-01. During the preparation of this paper the second named author was partially supported by a Pionier grant of the Netherlands Organization for Scientific Research (NWO). He also enjoy...