International Conference on Integral Geometry, Harmonic Analysis and Representation Theory in honor of Sigurdur Helgason on the occasion of his 80th birthday. Reykjavik, Iceland, 15-18 August 2007.

The Plancherel formula for Riemannian symmetric spacesG/Khas two distinguishing features:a) There is no discrete spectrum,

b) The spectrum is multiplicity-free.As one of the descendants of Helgason's works on Riemannian symmetric spaces

G/K, I consider the following scheme:

Symmetric pair Analysis Branching Riemannian G/KG↓KSemisimple G/HG↓HIn this talk, I plan to give some new perspectives to the aforementioned properties (a) and (b) from the following two viewpoints:

A) Branching to semisimple symmetric pairs.

B) Propagation of multiplicty-free propropeties.

[ lecture notes ]

© Toshiyuki Kobayashi