A property of isometric mappings between dual polar spaces of type DQ2n,KReport as inadecuate




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(2010)ANNALS OF COMBINATORICS.14(3).p.307-318 Mark abstract Let f be an isometric embedding of the dual polar space Delta = DQ(2n, K) into Delta' = DQ(2n, K'). Let P denote the point-set of Delta and let e' : Delta' -> Sigma' congruent to PG(2(n) - 1, K') denote the spin-embedding of Delta'. We show that for every locally singular hyperplane H of Delta, there exists a unique locally singular hyperplane H' of Delta' such that f(H) = f(P) boolean AND H'. We use this to show that there exists a subgeometry Sigma congruent to PG(2(n) - 1, K) of Sigma' such that: (i) e' circle f (x) is an element of Sigma for every point x of Delta; (ii) e := e' circle f defines a full embedding of Delta into Sigma, which is isomorphic to the spin-embedding of Delta.

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1108477



Author: Bart De Bruyn

Source: https://biblio.ugent.be/publication/1108477



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