The Plancherel formula for Riemannian symmetric spaces G/K has 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/K G ↓ K Semisimple G/H G ↓ H
In 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