Regular Representations on Homogeneous Spaces (opening lecture). RIMS Workshop: Developments in Representation Theory and Related Topics. RIMS, Kyoto University, 9-12 July 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h for L(X)?
We highlight “multiplicities” and “temperdness” for these questions, and give their geometric criteria.

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

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© Toshiyuki Kobayashi