Functional Analysis and Applications Seminar 

21/12/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Rui Palma, Oslo and CEAF

Hecke algebras and their $C^{*}$-completions

Hecke algebras can be seen as an analogue of group algebras of quotient groups $G/H$ when $H$ is no longer a normal subgroup. They admit several canonical $C^{*}$-completions and when some of these coincide, and a maximal $C^{*}$-norm exists, there is a nice correspondence between $C^{*}$-representations of a Hecke algebra and unitary representations of $G$ generated by the $H$-fixed vectors. In this seminar I will give an overview of the theory of Hecke algebras and their various $C^{*}$-completions. I will also discuss some recent work on the existence of a maximal $C^{*}$-completion and the isomorphism problem among the remaining canonical completions, for several classes of Hecke algebras.