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) -pseudoconvex exhaustion of the associated open orbit, where is the complex dimension of the cycles under consideration.
@article{ASNSP_2010_5_9_3_573_0,
author = {Huckleberry, Alan and Wolf, Joseph},
title = {Cycle space constructions for exhaustions of flag domains},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {573--580},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {3},
year = {2010},
mrnumber = {2722656},
zbl = {1209.32019},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_3_573_0/}
}
TY - JOUR AU - Huckleberry, Alan AU - Wolf, Joseph TI - Cycle space constructions for exhaustions of flag domains JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 573 EP - 580 VL - 9 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_3_573_0/ LA - en ID - ASNSP_2010_5_9_3_573_0 ER -
%0 Journal Article %A Huckleberry, Alan %A Wolf, Joseph %T Cycle space constructions for exhaustions of flag domains %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 573-580 %V 9 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_3_573_0/ %G en %F ASNSP_2010_5_9_3_573_0
Huckleberry, Alan; Wolf, Joseph. Cycle space constructions for exhaustions of flag domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 573-580. http://www.numdam.org/item/ASNSP_2010_5_9_3_573_0/
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