The uniqueness of the SDPS-set of the symplectic dual polar space ,

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 [B. De Bruyn, P. Vandecasteele, Valuations and hyperplanes of dual polar spaces, J. Combin. Theory Ser. A 112 (2005) 194–211] 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 D W ( 4 n − 1 , q ) , n ≥ 2 , has up to isomorphisms a unique SDPS-set.