On the classification of irreducible representations of affine Hecke algebras with unequal parameters

By M. Solleveld. 2010

57 citations recorded by the source corpus.

Introduction 31 Preliminaries 101.1 Root systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Affine Hecke algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 Graded Hecke algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Parabolic subalgebras . . . . . . . . . . . . . . . . . . . . . . . . . . 151.5 Analytic localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.6 The relation with reductive p-adic groups . . . . . . . . . . . . . . . 192 Classification of irreducible representations 242.1 Two reduction theorems . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 The Langlands classification . . . . . . . . . . . . . . . . . . . . . . . 282.3 An affine Springer correspondence . . . . . . . . . . . . . . . . . . . 353 Parabolically induced representations 373.1 Unitary representations and intertwining operators . . . . . . . . . . 383.2 The Schwartz algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3 Parametrization of representations with induction data . . . . . . . . 483.4 The geometry of the dual space . . . . . . . . . . . . . . . . . . . . . 524 Parameter deformations 584.1 Scaling Hecke algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Preserving unitarity . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3 Scaling intertwining operators . . . . . . . . . . . . . . . . . . . . . . 684.4 Scaling Schwartz algebras . . . . . . . . . . . . . . . . . . . . . . . . 725 Noncommutative geometry 775.1 Topological K-theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Periodic cyclic homology . . . . . . . . . . . . . . . . . . . . . . . . . 835.3 Weakly spectrum preserving morphisms . . . . . . . . . . . . . . . . 855.4 The Aubert–Baum–Plymen conjecture . . . . . . . . . . . . . . . . . 885.5 Example: type C

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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