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

Published electronically:
August 3, 2000

MathSciNet review:
1422608

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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**, 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:
http://dx.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