To a real reductive symmetric space $G/H$, we may associate one and often two C_-algebras. The first corresponds to the support of the Plancherel measure for the regular representation on $L^2(G/H)$, while the second corresponds to the subset of the support consisting of irreducible representations that admit $H$-fixed distributions. The latter C_-algebra exists for favorable classes of symmetric spaces.
We investigate the structure and properties of these $C^*$-algebras, leveraging the established Plancherel theory for $G/H$: the Plancherel decomposition developed by Erik van den Ban, Patrick Delorme, and Henrik Schlichtkrull, as well as the theory of discrete series representations, as studied by Flensted-Jensen, Oshima--Matsuki, Schlichtkrull, and others. We also discuss subtle aspects that seem not immediate from these results.
This is joint work with A. Afgoustidis, N. Higson, P. Hochs, and Y. Song.
By Shintaro Nishikawa
By Juliette Coutens
By Yiannis Sakellaridis
By Bernhard Krötz
By Yoshiki Oshima
By Yiannis Sakellaridis
By Bernhard Krötz
By Polyxeni Spilioti
By Alain Connes
By Karl-Hermann Neeb
By Karl-Hermann Neeb
