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Spaces ofp-vectors of bounded rank

Authors:	Boaz Gelbord Roy Meshulam

Institution:	(1) Department of Mathematics, Technion — Israel Institute of Technology, 32000 Haifa, Israel

Abstract:	LetV be ann-dimensional space over an infinite field of characteristic different from 2. Therank ofw ∈ Λ^p V is the minimal dimension of a subspaceU ⊂V such thatw ∈ Λ^p U. Extending a well-known result on linear spaces in the Grassmannian, it is shown that ifp≤k<n then the maximal dimension of a subspaceW ⊂ Λ^p V such that rankw≤k for allω ∈W is $\max \left\{ {\left( {_{ p}^{k + \in } } \right),\left( {_p^m } \right) + \left( {k - m} \right)\left( {n - m} \right)} \right\}$ where∈=1 ifk=p orp=2\|k,∈=0 otherwise, andm satisfies $\left( {_{p - 1}^{m - 1} } \right) + m \leqslant k \leqslant \left( {_{p - 1}^{ m} } \right) + m$ . Supported by The Israel Science Foundation founded by the Academy of Sciences and Humanities.

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