Regular Representations on Homogeneous Spaces. Dynamics of Group Actions: a conference in honor of Yves Benoist. Cetraro, Italy, 27-31 May 2019.

I plan to discuss some basic questions about regular representations on X acted algebraically by real reductive groups G.
  1. (function spaces) Does the group G have a ''good control” on the space C(X) of function on X?
  2. (L2 theory) What can we say about ''spectrum” for L(X)?
We highlight ''multiplicities” and ''temperdness” for these questions, and give their geometric criteria.

The second topic is a joint work with Yves Benoist.

If time permits, I will mention some applications to branching problems for restriction of infinite-dimensional representations.

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© Toshiyuki Kobayashi