## T. Kobayashi,

*Multiplicity-free theorems of the restrictions of unitary
highest weight modules with respect to reductive symmetric pairs*,

Representation Theory and Automorphic Forms,
Progress in Math. **255**, Birkhäuser, 2007, pp. 45-109. math.RT/0607002..

The complex analytic methods have found a wide range of applications in the
study of multiplicity-free representations. This article discusses, in
particular, its applications to the question of restricting highest weight
modules with respect to reductive symmetric pairs. We present a number of
multiplicity-free branching theorems that include the multiplicity-free
property of some of known results such as the Clebsh-Gordan-Pieri
formula for
tensor products, the Plancherel theorem for Hermitian symmetric spaces (also
for line bundle cases), the Hua-Kostant-Schmid *K*-type formula, and the
canonical representations in the sense of Vershik-Gelfand-Graev. Our method
works in a uniform manner for both finite and infinite dimensional cases, for
both discrete and continuous spectra, and for both classical and exceptional
cases.

[
arXiv |
RIMS preprint(pdf) |
RIMS preprint(ps.gz) |
preprint version(pdf) |
preprint version(dvi) |
SpringerLink |
related papers ]

The original publication is available at www.springerlink.com.

© Toshiyuki Kobayashi