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.
Representation Theory and Automorphic Forms

[ 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.

Home EnHome Jp

© Toshiyuki Kobayashi