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The natural representation of the stabilizer of four subspaces

2000
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Transactions of the American Mathematical Society
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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. Then the mapping α has kernel A ⊕ B , and the induced map is an

doi:10.1090/s0002-9947-00-01959-0
fatcat:bu32r6l3j5dcrbhy2e4zdvwzti