The uniqueness of the SDPS-set of the symplectic dual polar space $DW(4n-1,q)$, $n \geq 2$

Abstract

SDPS-sets are very nice sets of points in dual polar spaces which themselves carry the structure of dual polar spaces. They were introduced in \cite{DB-V:2} because they gave rise to new valuations and hyperplanes of dual polar spaces. In the present paper, we show that the symplectic dual polar space (4n-1,q)$, \geq 2$, has up to isomorphisms a unique SDPS-set