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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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:

Consider the natural action of the general linear group $GL(V)$ on the product of four Grassmann varieties of the vector space $V$. In General linear group action on four Grassmannians we gave an algorithm to construct the generic stabilizer $H$ of this action. In this paper we investigate the structure of $V$ as an $H$-module, and we show the effectiveness of the methods developed there, by applying them to the explicit description of $H$.


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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
PII: S 0002-9947(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