Geometric Hyperplanes of the Near Hexagon L_3 times GQ(2, 2)

Metod Saniga (1, 2) , Peter Levay (2, 3) , Michel R. P. Planat (2, 4) , Petr Pracna (2, 5)

1 Astronomical Institute of the Slovak Academy of Sciences
2 Center for Interdisciplinary Research (ZiF)
3 BME - Budapest University of Technology and Economics [Budapest]
4 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
5 JH-INST - J. Heyrovsky Institute of Physical Chemistry

Having in mind their potential quantum physical applications, we classify all geometric hyperplanes of the near hexagon that is a direct product of a line of size three and the generalized quadrangle of order two. There are eight different kinds of them, totalling to 1023 = 2^{10} - 1 = |PG(9, 2)|, and they form two distinct families intricately related with the points and lines of the Veldkamp space of the quadrangle in question.

Mots clés: Near Hexagons; Geometric Hyperplanes; Veldkamp Spaces; Qubits

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Metod Saniga, Peter Levay, Michel R. P. Planat, Petr Pracna. Geometric Hyperplanes of the Near Hexagon L_3 times GQ(2, 2). Letters in Mathematical Physics, 2010, 91, pp.93-104. ⟨10.1007/s11005-009-0362-z⟩. ⟨hal-00410681v2⟩