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On the Universal Embedding of Dual Polar Spaces of Type Sp2n(2)

โœ Scribed by Phillip McClurg

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
166 KB
Volume
90
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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 subspaces of a fixed vector space of dimension n. This is accomplished by studying the nullity of associated incidence matrices over GF(2). In the process we provide evidence of a generating set for the dual polar space of type Sp 2n (2) of cardinality *(n).

๐Ÿ“œ SIMILAR VOLUMES

On the Universal Embedding of the Sp2n(2
On the Universal Embedding of the Sp2n(2) Dual Polar Space
โœ Paul Li ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 162 KB

A. E. Brouwer has shown that the universal embedding of the Sp 2n (2) dual polar space has dimension at least (2 n +1)(2 n&1 +1)ร‚3 and has conjectured equality. The present paper settles this conjecture in the affirmative by proving a theorem about permutation modules for GL n (2) which implies the

On the Universal Embedding of the U2n(2)
On the Universal Embedding of the U2n(2) Dual Polar Space
โœ Paul Li ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 349 KB

A. E. Brouwer has shown that the universal embedding of the U 2n (2) dual polar space has dimension at least (4 n +2)/3 and has conjectured equality. The present paper proves this conjecture by establishing a related result about permutation modules for GL n (4). The method is the same used in the a

On the Generation of Some Dual Polar Spa
On the Generation of Some Dual Polar Spaces of Symplectic Type OverGF(2)
โœ B.N. Cooperstein ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 171 KB

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).

On the Generation of Dual Polar Spaces o
On the Generation of Dual Polar Spaces of Unitary Type Over Finite Fields
โœ B.N Cooperstein ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 143 KB

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.

On the Generation of Dual Polar Spaces o
On the Generation of Dual Polar Spaces of Symplectic Type over Finite Fields
โœ B.N Cooperstein ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 326 KB

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-