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On the Universal Embedding of the U2n(2) Dual Polar Space

โœ Scribed by Paul Li

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
349 KB
Volume
98
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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 author's previous paper on an analogous question for the Sp 2n (2) dual polar space.

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 Dual Polar
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โœ Phillip McClurg ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 166 KB

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

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-