It is demonstrated that the dual polar space of type Sp 2n (q), q>2, can be generated as a geometry by ( 2n n )&( 2n n&2 ) points. 1998 Academic Press ## 1. Introduction We assume the reader is familiar with the basic definitions relating to undirected graphs and linear incidence system or point-
On the Generation of Dual Polar Spaces of Unitary Type Over Finite Fields
โ Scribed by B.N Cooperstein
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 143 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0195-6698
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โฆ Synopsis
It is demonstrated that the generating rank of the dual polar space of type U 2n (q 2 ) is 2n n when q > 2. It is also shown that this is equal to the embedding rank of this geometry.
๐ SIMILAR VOLUMES
It is demonstrated that the dual polar space of type Sp(2n, 2) can be generated as a geometry by 3 points when n = 4 and 5. In the latter case this affirmatively resolves a conjecture of Brouwer that the dimension of the universal projective embedding of this geometry is ฮป(5).
It has been conjectured by A. E. Brouwer that the dimension of the universal embedding module of a dual polar space of type Sp 2n (2) is Following a point stabilizer approach of A. A. Ivanov and M. K. Bardoe, we investigate the dimensions of certain quotients of permutation modules for SL n (2) on
Let be a finite thick dual polar space, and let H be a hyperplane of . Calling the elements of of type 2 quads, we call a quad ฮฑ โ H singular (respectively subquadrangular or ovoidal) if H meets ฮฑ in the perp of a point (respectively in a full subquadrangle or in an ovoid). A hyperplane is said to b
## B as a modular constituent with non-zero multiplicity. This result suggests that we should investigate the decomposition modulo 2 of the irreducible characters in 1 G when G is a group of Lie type of odd characteristic and B see which real-valued irreducible Brauer characters occur as constitue