The generating rank of the unitary and symplectic Grassmannians

2010/10/01 by Rieuwert J. Blok, Blok, Rieuwert J., Bruce N. Cooperstein +1
Mathematics · #05A15 #51A45 (Secondary) #51A50 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05A15 #msc:51A45 #msc:51A50

paper · pdf · doi:10.48550/arxiv.1010.0205

arxiv created 2010/10/01 · arxiv updated 2010/10/04

Abstract

We prove that the Grassmannian of totally isotropic k-spaces of the polar space associated to the unitary group SU_2n(\mathbbF) (n∈ ℕ) has generating rank 2n\choose k when \mathbbF≠ \mathbbF₄. We also reprove the main result of Blok [Blok2007], namely that the Grassmannian of totally isotropic k-spaces associated to the symplectic group Sp_2n(\mathbbF) has generating rank 2n\choose k-2n\choose k-2, when \rmChar(\mathbbF)≠ 2.

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