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# Dual polar spaces of arbitrary rank

(2011) 11(3). p.471-508
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Organization
Abstract
In 1982 P. Cameron gave a characterisation of dual polar spaces of finite rank viewed as point-line spaces. This characterisation makes essential use of the fact that dual polar spaces of finite rank have finite diameter. Our goal is to give a characterisation which includes dual polar spaces of infinite rank. Since dual polar spaces of infinite rank are disconnected, we introduce a point-relation that denotes pairs of points at "maximal distance", and we call this an opposition relation. This approach is in the spirit of the theory of twin buildings.

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## Citation

Chicago
Huggenberger, Simon. 2011. “Dual Polar Spaces of Arbitrary Rank.” Advances in Geometry 11 (3): 471–508.
APA
Huggenberger, S. (2011). Dual polar spaces of arbitrary rank. ADVANCES IN GEOMETRY, 11(3), 471–508.
Vancouver
1.
Huggenberger S. Dual polar spaces of arbitrary rank. ADVANCES IN GEOMETRY. 2011;11(3):471–508.
MLA
Huggenberger, Simon. “Dual Polar Spaces of Arbitrary Rank.” ADVANCES IN GEOMETRY 11.3 (2011): 471–508. Print.
```@article{1255874,
abstract     = {In 1982 P. Cameron gave a characterisation of dual polar spaces of finite rank viewed as point-line spaces. This characterisation makes essential use of the fact that dual polar spaces of finite rank have finite diameter. Our goal is to give a characterisation which includes dual polar spaces of infinite rank. Since dual polar spaces of infinite rank are disconnected, we introduce a point-relation that denotes pairs of points at {\textacutedbl}maximal distance{\textacutedbl}, and we call this an opposition relation. This approach is in the spirit of the theory of twin buildings.},
author       = {Huggenberger, Simon},
issn         = {1615-715X},
language     = {eng},
number       = {3},
pages        = {471--508},
title        = {Dual polar spaces of arbitrary rank},