Regular Representations on Homogeneous Spaces (opening lecture). 13-th edition of the International Workshop: Lie Theory and Its Applications in Physics (LT-13). Varna, Blugaria, 17-23 June 2019.

I plan to discuss some fundamental problems about regular representations on X acted by reductive Lie 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 L2(X)?
We highlight ''multiplicities” and ''temperdness” for these questions, and give their geometric criteria.

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

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© Toshiyuki Kobayashi