A property of isometric mappings between dual polar spaces of type DQ(2n,K)
 Author
 Bart De Bruyn (UGent)
 Organization
 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 pointset of Delta and let e' : Delta' > Sigma' congruent to PG(2(n)  1, K') denote the spinembedding 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 spinembedding of Delta.
 Keywords
 dual polar space, isometric embedding, hyperplane, spinembedding, SPINEMBEDDINGS, HYPERPLANES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU1108477
 Chicago
 De Bruyn, Bart. 2010. “A Property of Isometric Mappings Between Dual Polar Spaces of Type DQ(2n,K).” Annals of Combinatorics 14 (3): 307–318.
 APA
 De Bruyn, B. (2010). A property of isometric mappings between dual polar spaces of type DQ(2n,K). ANNALS OF COMBINATORICS, 14(3), 307–318.
 Vancouver
 1.De Bruyn B. A property of isometric mappings between dual polar spaces of type DQ(2n,K). ANNALS OF COMBINATORICS. 2010;14(3):307–18.
 MLA
 De Bruyn, Bart. “A Property of Isometric Mappings Between Dual Polar Spaces of Type DQ(2n,K).” ANNALS OF COMBINATORICS 14.3 (2010): 307–318. Print.
@article{1108477, 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 pointset of Delta and let e' : Delta' {\textrangle} Sigma' congruent to PG(2(n)  1, K') denote the spinembedding 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 spinembedding of Delta.}, author = {De Bruyn, Bart}, issn = {02180006}, journal = {ANNALS OF COMBINATORICS}, keyword = {dual polar space,isometric embedding,hyperplane,spinembedding,SPINEMBEDDINGS,HYPERPLANES}, language = {eng}, number = {3}, pages = {307318}, title = {A property of isometric mappings between dual polar spaces of type DQ(2n,K)}, url = {http://dx.doi.org/10.1007/s0002601000616}, volume = {14}, year = {2010}, }
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