Cycle space constructions for exhaustions of flag domains

Huckleberry, Alan¹  ; Wolf, Joseph² 

¹ Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
² Department of Mathematics, University of California, Berkeley, California, 94720-3840, U.S.A.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 573-580

Résumé

A real semisimple group has only finitely many orbits on every flag manifold of its complexification. To each of these orbits there is a naturally associated space of algebraic cycles, and that cycle space is known to be a Stein manifold. In the past, properties of the cycle space have been proved by transforming functions or cohomology from, e.g., an open orbit in the flag manifold to its cycle space. Here the opposite is done: given an irreducible representation of a maximal compact subgroup of the real semisimple group, a canonical strictly plurisubharmonic exhaustion of the cycle space is constructed. This is then transformed to a (continuous) $q$-pseudoconvex exhaustion of the associated open orbit, where $q$ is the complex dimension of the cycles under consideration.

Détail

Classification : 32M05, 32F10, 32M10, 22E46