A Hecke algebra isomorphism over close local fields

Iwahori-hecke Algebras of Sl2 over 2-dimensional Local Fields

Hecke algebras were first studied because of their role in the representation theory of p-adic groups, or algebraic groups over 1-dimensional local fields. There are two important classes of Hecke algebras. One is spherical Hecke algebras attached to maximal compact open subgroups, and the other is Iwahori-Hecke algebras attached to Iwahori subgroups. A spherical Hecke algebra is isomorphic to ...

Semigroups over Local fields

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

The affine Hecke algebra

1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...

Hecke Algebra Characters

Hecke Algebras of Classical Groups over p-adic Fields II

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G de¢ned over p-adic ¢elds in order to understand their admissible representations. EachHecke algebra is associated to a pair …JS; rS†of an open compact subgroup JS and its irreducible representation rSwhich is constructed fromgiven dataS ˆ …G;P0 0; R†. Here, G is a semisimple element in...