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