Nearly all subspaces of a classical polar space arise from its universal embedding.

@article{Cardinali2020NearlyAS,
  title={Nearly all subspaces of a classical polar space arise from its universal embedding.},
  author={Ilaria Cardinali and Luca Giuzzi and Antonio Pasini},
  journal={arXiv: Representation Theory},
  year={2020}
}
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Characterizations of symplectic polar spaces
A polar space S is said to be symplectic if it admits an embedding ε : S → PG( V ) such that the ε -image ε ( S ) of S is defined by an alternating form of V . In this paper we characterize symplectic…

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