Symmetry in Nonlinear Mathematical Physics - 2009

Yuriy Dzyadyk (Glushkov Cybernetic Center, Kyiv, Ukraine)

Induced representations on symmetric and spherical spaces

Abstract:
1. Main results about induced representations over symmetric spaces – Satake schemes, localization theorem, reduction theorem, local subgroups Gα, Gαβ, structure of subgroup M, the rốle of the Iwasawa decomposition, Bruhat decomposition of the symmetric spaces etc.

History: É. Cartan (1929), A. Kirillov (1957, 1960), I. Satake (1960), M. Sugiura (1962), I. Gel'fand (1974), Yu. Dzyadyk (1975).

2. Landmarks in the history of spherical spaces: Yu. Dzyadyk (1975), M. Krämer (1978, published in 1979), E. Vinberg and B. Kimel'fel'd (1978), I. Mikityuk (1985), M. Brion (1985) etc.

3. Addenda to the theory of spherical spaces: exhaustive classification of spherical spaces, Kac schemes of some spherical spaces.

4. Some results and problems about induced representations over spherical spaces.