Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

The natural representation of the stabilizer of four subspaces

Author(s): Jozsef Horvath; Roger Howe
Journal: Trans. Amer. Math. Soc. 352 (2000), 5795-5815.
MSC (1991): Primary 20G05; Secondary 14L30, 15A69, 16G20
Posted: August 3, 2000
MathSciNet review: 1422608
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Abstract:

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 .

References:

1.: I.M. Gelfand and V.A. Ponomarev, Problems of linear algebra and classification of quadruples of subspaces in a finite dimensional vector space, Coll. Math. Soc. Bolyai, Tihany (Hungary) North-Holland, 1972, pp. 163-237. MR 50:9896
2.: J. Horvath and R. Howe, General linear group action on four Grassmannians, submitted to Mathematische Zeitschrift.
3.: V. Kac, Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57-92. MR 82j:16050
4.: L.A. Nazarova, Representations of quadruples, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 1361-1377. MR 36:6400

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