C' by the formula a . v = x(a)v for a E Ko, v E P2. 3. We will use the following terminology (modeled after the associated real symmetric spaces) for complex symmetric pairs. If ~ is a complex semisimple R. Brylinski and B. K ostant 20 Lie algebra then the fixed space to C t of a complex Lie algebra involution a is called a symmetric subalgebra. Then to is reductive in t. The complex Cartan decomposition is then t = to + s where set is the (-1 )-eigenspace of a.
Functional Analysis on the Eve of the 21st Century: Volume I: In Honor of the Eightieth Birthday of I. M. Gelfand by Kazuhiko Aomoto (auth.), Simon Gindikin, James Lepowsky, Robert L. Wilson (eds.)