Arrangements in unitary and orthogonal geometry over finite fields

DOI10.1016/0097-3165(85)90072-XzbMath0579.51005MaRDI QIDQ1067206

Peter Orlik, Louis Solomon

Publication date: 1985

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

zbMATH Keywords

characteristic polynomialgeometric latticemonic polynomialWitt indexintersections of non-isotropic hyperplanes

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35) General binary quadratic forms (11E16) Lattices of subspaces and geometric closure systems (51D25)

Related Items

An arrangement in orthogonal geometry over finite field of Char=2 ⋮ Lattices generated by strongly closed subgraphs in \(d\)-bounded distance-regular graphs ⋮ Lattices generated by two orbits of subspaces under finite singular symplectic groups ⋮ Lattices generated by transitive sets of subspaces under finite classical groups I ⋮ Geometry of classical groups over finite fields and its applications ⋮ Lattices generated by joins of the flats in orbits under finite affine-singular symplectic group and its characteristic polynomials ⋮ Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials ⋮ Lattices generated by join of strongly closed subgraphs in \(d\)-bounded distance-regular graphs ⋮ Lattices Generated by Two Orbits of Subspaces Under Finite Singular Classical Groups ⋮ Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials ⋮ Reflection Groups ⋮ Lattices generated by subspaces in \(d\)-bounded distance-regular graphs ⋮ Lattices generated by two orbits of subspaces under finite classical groups ⋮ Lattices generated by orbits of flats under finite affine-symplectic groups ⋮ Lattices generated by subspaces of the same dimension and rank in orthogonal geometry over finite fields of odd characteristic

Cites Work

• A character formula for the unitary group over a finite field
• Unitary reflection groups and cohomology
• A Fixed-Point Formula for the Classical Groups Over a Finite Field
• On the Decomposition of Orthogonalities into Symmetries
• Finite Unitary Reflection Groups
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