2013/07/09 by Wen Liu, Liu, Wen, Mark Pankov +3
Computer Science · Mathematics · #51A50 #51E20 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1307.2316
openalex publication_date 2013/07/09 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Let Π be a polar space of rank n≥ 3. Denote by \mathcal Gk(Π) the polar Grassmannian formed by singular subspaces of Π whose projective dimension is equal to k. Suppose that k is an integer not greater than n-2 and consider the relation \mathfrak Ri,j, 0≤ i≤ j≤ k+1 formed by all pairs (X,Y)∈ \mathcal Gk(Π)× \mathcal Gk(Π) such that dimp(X⊥∩ Y)=k-i and dimp (X∩ Y)=k-j (X⊥ consists of all points of Π collinear to every point of X). We show that every bijective transformation of \mathcal Gk(Π) preserving \mathfrak R1,1 is induced by an automorphism of Π and the same holds for the relation \mathfrak R0,t if n≥ 2t≥ 4 and k=n-t-1. In the case when Π is a finite classical polar space, we establish that the valencies of \mathfrak Ri,j and \mathfrak Ri',j' are distinct if (i,j)≠ (i',j').