The natural representation of the stabilizer of four subspaces
Authors:
Jozsef Horvath and Roger Howe
Journal:
Trans. Amer. Math. Soc. 352 (2000), 5795-5815
MSC (1991):
Primary 20G05; Secondary 14L30, 15A69, 16G20
DOI:
https://doi.org/10.1090/S0002-9947-00-01959-0
Published electronically:
August 3, 2000
MathSciNet review:
1422608
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Consider the natural action of the general linear group 
on the product of four Grassmann varieties of the vector space 
. In General linear group action on four Grassmannians we gave an algorithm to construct the generic stabilizer 
of this action. In this paper we investigate the structure of 
as an 
-module, and we show the effectiveness of the methods developed there, by applying them to the explicit description of 
.
- 1. I. M. Gel′fand and V. A. Ponomarev, Problems of linear algebra and classification of quadruples of subspaces in a finite-dimensional vector space, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970) North-Holland, Amsterdam, 1972, pp. 163–237. Colloq. Math. Soc. János Bolyai, 5. MR 0357428
- 2. J. Horvath and R. Howe, General linear group action on four Grassmannians, submitted to Mathematische Zeitschrift.
- 3. V. G. Kac, Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), no. 1, 57–92. MR 557581, https://doi.org/10.1007/BF01403155
- 4. L. A. Nazarova, Representations of a tetrad, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 1361–1378 (Russian). MR 0223352
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Additional Information
Jozsef Horvath
Affiliation:
Department of Mathematics, West Chester University, West Chester, Pennsylvania 19383
Roger Howe
Affiliation:
Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, Connecticut 06520-8283
DOI:
https://doi.org/10.1090/S0002-9947-00-01959-0
Received by editor(s):
June 21, 1996
Published electronically:
August 3, 2000
Additional Notes:
Research partially supported by NSF grant DMS-9224358
Article copyright:
© Copyright 2000
American Mathematical Society
