The generating rank of the unitary and symplectic Grassmannians

Authors:
Rieuwert J. Blok;Bruce N. Cooperstein
Affiliations:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;Department of Mathematics, University of California, Santa Cruz, CA, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2012

Citing 4
Cited 1

On the generation of dual polar spaces of unitary type over finite fields

European Journal of Combinatorics
On the generation of dual polar spaces of symplectic type over finite fields

Journal of Combinatorial Theory Series A
The generating rank of the symplectic grassmannians: Hyperbolic and isotropic geometry

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Highest weight modules and polarized embeddings of shadow spaces

Journal of Algebraic Combinatorics: An International Journal

On the nucleus of the Grassmann embedding of the symplectic dual polar space DSp(2n,F), char(F)=2

European Journal of Combinatorics

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Abstract

We prove that the Grassmannian of totally isotropic k-spaces of the polar space associated to the unitary group SU"2"n(F) (n@?N) has generating rank (2nk) when FF"4. We also reprove the main result of Blok (2007) [3], namely that the Grassmannian of totally isotropic k-spaces associated to the symplectic group Sp"2"n(F) has generating rank (2nk)-(2nk-2), when Char(F)2.