Two new classes of hyperplanes of the dual polar space not arising from the Grassmann embedding

✍ Scribed by Bart De Bruyn

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 230 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.05.036

✦ Synopsis

Let n (q) denote the geometry of the hyperbolic lines of the symplectic polar space W (2n -1, q), n 2. We show that every hyperplane of n (q) gives rise to a hyperplane of the Hermitian dual polar space DH (2n -1, q 2 ). In this way we obtain two new classes of hyperplanes of DH (2n -1, 4) which do not arise from the Grassmann embedding of DH (2n -1, 4).