Parametrizing maximal compact subvarieties

Author:
Jodie D. Novak

Journal:
Proc. Amer. Math. Soc. **124** (1996), 969-975

MSC (1991):
Primary 22E46; Secondary 22E45

DOI:
https://doi.org/10.1090/S0002-9939-96-03153-X

MathSciNet review:
1301042

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For the Lie group , let be the open orbit of Lagrangian planes of signature in the generalized flag variety of Lagrangian planes in . For a suitably chosen maximal compact subgroup of and a base point we have that the orbit of is a maximal compact subvariety of . We show that for the connected component containing in the space of translates of which lie in is biholomorphic to , where denotes with the opposite complex structure.

**[BE]**R. J. Baston and M. G. Eastwood,*The Penrose transform: Its interaction with representation theory*, Clarendon Press, Oxford, 1989. MR**92j:32112****[DZ]**E. G. Dunne and R. Zierau,*Twistor theory for indefinite Kähler symmetric spaces*,

Contemp. Math., vol. 154, Amer. Math. Soc., Providence, RI, 1993, pp. 117--132 . MR**95d:22013****[K]**A.W. Knapp,*Representation theory of semisimple groups*, Princeton Math. Ser., no. 36, Princeton University Press, Princeton, NJ, 1986. MR**87j:22022****[PR]**C. M. Patton and H. Rossi,*Unitary structures on cohomology*, Trans. Amer. Math. Soc.**290**(1985), 235--258. MR**87g:22014****[PR1]**------,*Cohomology on complex homogeneous manifolds with compact subvarieties*, Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1986, pp. 199--211. MR**88a:32037****[SW]**W. Schmid and J. A. Wolf,*A vanishing theorem for open orbits on complex flag manifolds*, Proc. Amer. Math. Soc.**92**(1984), 461--464. MR**85i:32029****[We]**R. O. Wells,*Parametrizing the compact submanifolds of a period matrix domain by a Stein manifold*, Symposium on Several Complex Variables, Park City, Utah, 1970 (R. M. Brooks, ed), Lecture Notes in Math., vol. 184, Springer-Verlag, New York, 1971, pp. 121--150. MR**46:7555****[WW]**R. O. Wells and J. A. Wolf,*Poincaré series and automorphic cohomology on flag domains*, Ann. of Math. (2)**105**(1977), 397--448. MR**56:5955****[W]**J. A. Wolf,*Fine structure of Hermitian symmetric spaces*, Pure Appl. Math.**8**(1972), 271--357. MR**53:8516****[W1]**------,*The Stein condition for cycle spaces of open orbits on complex flag manifolds*, Ann. of Math. (2)**136**(1992), 541--555. MR**93m:32045**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
22E46,
22E45

Retrieve articles in all journals with MSC (1991): 22E46, 22E45

Additional Information

**Jodie D. Novak**

Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613

Address at time of publication:
Department of Mathematical Sciences, Ball State University, Muncie,Indiana 47303

Email:
novak@math.bsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03153-X

Keywords:
Generalized flag variety,
Penrose transform,
symplectic group

Received by editor(s):
August 16, 1994

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1996
American Mathematical Society