International Mathematics Research Papers - recent issues

AF-Embeddings of the Crossed Products of AH-Algebras by Finitely Generated Abelian Groups

Lin, H. — 2008-08-27

Let X be a compact metric space and let be a Z^k (k ≥ 1) action on X. We give a solution to a version of Voiculescu's problem of AF-embedding: The crossed product C(X) Z^k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive -invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let : G -> Aut(C) be a monomorphism. We show that C G can be embedded into a unital simple AF-algebra if and only if C admits a faithful -invariant tracial state.

Quiver Varieties, Category for Rational Cherednik Algebras, and Hecke Algebras

Gordon, I. G. — 2008-08-23

Distinguished Tame Supercuspidal Representations

Hakim, J., Murnaghan, F. — 2008-06-04

This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary conditions for a tame supercuspidal representation of G to be distinguished by (the fixed points of) an involution of G are expressed in terms of properties of the G-orbit of the associated G-datum. When these conditions are satisfied, the question of whether a tame supercuspidal representation is distinguished reduces to the question of whether certain cuspidal representations of finite groups of Lie type are distinguished relative to particular quadratic characters. As an application of the main results, we obtain necessary and sufficient conditions for equivalence of two of Yu's supercuspidal representations associated to distinct G-data.