Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-00-01959-0
Published electronically: August 3, 2000
MathSciNet review: 1422608
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $H$.


References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20G05, 14L30, 15A69, 16G20

Retrieve articles in all journals with MSC (1991): 20G05, 14L30, 15A69, 16G20


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

American Mathematical Society