Branchings to Symmetric Pairs and Analysis on Symmetric Spaces.
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 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

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 ]

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© Toshiyuki Kobayashi