HAL : hal-00409346, version 2

arXiv : 0908.0989

DOI : 10.1142/S021988781250082X

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International Journal of Geometric Methods in Modern Physics 10 (2013) 1250082

Versions disponibles :

v1 (07-08-2009)

v2 (15-08-2009)

The Veldkamp Space of the Smallest Slim Dense Near Hexagon

Richard M. Green 1, Metod Saniga 2

(2013)

We give a detailed description of the Veldkamp space of the smallest slim dense near hexagon. This space is isomorphic to PG(7, 2) and its 2^8 - 1 = 255 Veldkamp points (that is, geometric hyperplanes of the near hexagon) fall into five distinct classes, each of which is uniquely characterized by the number of points/lines as well as by a sequence of the cardinalities of points of given orders and/or that of (grid-)quads of given types. For each type we also give its weight, stabilizer group within the full automorphism group of the near hexagon and the total number of copies. The totality of (255 choose 2)/3 = 10795 Veldkamp lines split into 41 different types. We give a complete classification of them in terms of the properties of their cores (i. e., subconfigurations of points and lines common to all the three hyperplanes comprising a given Veldkamp line) and the types of the hyperplanes they are composed of. These findings may lend themselves into important physical applications, especially in view of recent emergence of a variety of closely related finite geometrical concepts linking quantum information with black holes.

1 :	Department of Mathematics, University of Colorado
	University of Colorado
2 :	Astronomical Institute, Slovak Academy of Sciences (ASTRINSTSAV)
	Astronomical Institute, Slovak Academy of Sciences

Domaine

:

Physique/Physique mathématique Mathématiques/Physique mathématique Physique/Physique Quantique Physique/Physique des Hautes Energies - Théorie

Mots Clés : Near Hexagons – Veldkamp Spaces – Quantum Information – Stringy Black Holes

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Contributeur : Metod Saniga <>

Soumis le : Samedi 15 Août 2009, 08:34:14

Dernière modification le : Mercredi 8 Août 2012, 14:40:22