Symmetry in Nonlinear Mathematical Physics - 2009

Yuriy Dzyadyk (Glushkov Cybernetic Center, Kyiv, Ukraine)

Induced representations on symmetric and spherical spaces

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.