The generating rank of a polar Grassmannian

2019/06/25 by Cardinali, Ilaria, Giuzzi, Luca, Pasini, Antonio
#14M15 #51B25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.10560

Abstract

In this paper we compute the generating rank of k-polar Grassmannians defined over commutative division rings. Among the new results, we compute the generating rank of k-Grassmannians arising from Hermitian forms of Witt index n defined over vector spaces of dimension N > 2n. We also study generating sets for the 2-Grassmannians arising from quadratic forms of Witt index n defined over V(N,\mathbb F_q) for q=4,8,9 and 2n ≤ N ≤ 2n+2. We prove that for N >6 they can be generated over the prime subfield, thus determining their generating rank.

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