In a celebrated paper by É. A. Vinberg and B. N. Kimelfeld (1978), a geometric characterization in terms of flag varieties was proved for the multiplicities of finite dimensional irreducible representations occurring in the induced/restricted representations to be not greater than one.[ programme ]
Unlike the finite dimensional case, multiplicities are often infinite in the irreducible decompositions for infinite dimensional representations, even in (seemingly) natural settings. In this talk, I plan to discuss finite multiplicity theorems and multiplicity-free theorems, in particular, for unitary representations as a descendant of Vinberg-Kimelfeld's work.
© Toshiyuki Kobayashi