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

 

Action on Grassmannians associated with a field extension


Author: Patrick Rabau
Journal: Trans. Amer. Math. Soc. 326 (1991), 127-155
MSC: Primary 05E05; Secondary 05A19, 05A30, 14L30, 33D15, 33D80
MathSciNet review: 1043863
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Abstract: We examine the action of the general linear group $ {\text{GL}}_L(V)$ on the set of all $ K$-subspaces of $ V$, where $ L/K$ is a finite field extension and $ V$ is a finite-dimensional vector space over $ L$. The orbits are completely classified in the case of quadratic and cubic extensions; for infinite fields, the number of orbits is shown to be infinite if the degree of the extension is at least four. As an application we obtain $ q$-analogues of tranformation and evaluation formulas for hypergeometric functions due to Gessel and Stanton.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1043863-0
PII: S 0002-9947(1991)1043863-0
Article copyright: © Copyright 1991 American Mathematical Society