Hyperplanes of dual polar spaces and the spin module

DOI10.1007/BF01194855zbMath0742.51003OpenAlexW1980489503MaRDI QIDQ811662

Ernest E. Shult, Joseph A. Thas

Publication date: 1992

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01194855

zbMATH Keywords

embeddingdual polar spacehyperplane sectionspin modulegeometric hyperplane

Mathematics Subject Classification ID

Generalized quadrangles and generalized polygons in finite geometry (51E12) Polar geometry, symplectic spaces, orthogonal spaces (51A50)

Related Items (16)

A characterization of a class of hyperplanes of \(DW(2n-1,\mathbb{F})\) ⋮ On the hyperplanes of the half-spin geometries and the dual polar spaces \(DQ(2n, \mathbb K)\) ⋮ The hyperplanes of \(DQ(2n, \mathbb K)\) and \(DQ^{ - }(2n+1,q)\) which arise from their spin-embeddings ⋮ Non-classical hyperplanes of finite thick dual polar spaces ⋮ Highest weight modules and polarized embeddings of shadow spaces ⋮ The hyperplanes of finite symplectic dual polar spaces which arise from projective embeddings ⋮ The structure of the spin-embeddings of dual polar spaces and related geometries ⋮ Hyperplanes of \(DW(2n-1,q)\), \(q\neq 2\), without ovoidal quads ⋮ Two classes of hyperplanes of dual polar spaces without subquadrangular quads ⋮ On the simple connectedness of hyperplane complements in dual polar spaces. II. ⋮ Hyperplanes of \(DW(5,{\mathbb{K}})\) with \({\mathbb{K}}\) a perfect field of characteristic 2 ⋮ Locally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces ⋮ On the simple connectedness of hyperplane complements in dual polar spaces ⋮ The hyperplanes of \(DW(5,2^h)\)which arise from embedding ⋮ Points and hyperplanes of the universal embedding space of the dual polar space DW\((5,q)\), \(q\) odd ⋮ The simple connectedness of hyperplane complements in thick dual polar spaces of rank at least 4

Cites Work

• Embeddings and hyperplanes of discrete geometries
• Gated sets in metric spaces
• Sheaves on buildings and modular representations of Chevalley groups
• Verallgemeinerte Vierecke in projektiven Räumen
• Dual polar spaces
• Geometric hyperplanes of embeddable Grassmannians
• Generalized quadrangles in projective spaces
• Buildings of spherical type and finite BN-pairs
• Geometric hyperplanes of the half-spin geometries arise from embeddings
• UNIVERSAL PROJECTIVE EMBEDDINGS OF THE GRASSMANNIAN, HALF SPINOR, AND DUAL ORTHOGONAL GEOMETRIES
• Unnamed Item

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