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

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

2009-08-24

arxiv.org/abs/0908.3363v2

Letters in Mathematical Physics 91 (2010) 93-104

Physics

Mathematical Physics

10 pages, 5 figures and 2 tables; Version 2 - more detailed discussion of the properties of hyperplanes

Scientific paper

10.1007/s11005-009-0362-z

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.

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