Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials

✍ Scribed by You Gao

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 232 KB
• Volume: 368
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(02)00674-2

✦ Synopsis

Let F (n+l) q 2 be the (n + l)-dimensional vector space over the finite field F q 2 , and U n+l,n (F q 2 ) the singular Unitary groups of degree n + l over F q 2 . Let M be any orbit of subspaces under U n+l,n (F q 2 ). Denote by L the set of subspaces which are intersections of subspaces in M, where the intersection of the empty set of subspaces of F (n+l) q 2 is assumed to be F (n+l) q 2 . By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice L, when the lattices form a geometric lattice, and the characteristic polynomial of L.