Isometric embeddings of polar Grassmannians and metric characterizations of their apartmentsReport as inadecuate




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Journal of Algebraic Combinatorics

, Volume 45, Issue 3, pp 777–801

First Online: 28 November 2016Received: 10 February 2015Accepted: 14 October 2016DOI: 10.1007-s10801-016-0724-4

Cite this article as: Kwiatkowski, M. & Pankov, M. J Algebr Comb 2017 45: 777. doi:10.1007-s10801-016-0724-4

Abstract

We describe isometric embeddings of polar Grassmann graphs formed by non-maximal singular subspaces. In almost all cases, they are induced by collinearity-preserving injections of polar spaces. As a simple consequence of this result, we get a metric characterization of apartments in polar Grassmannians.

KeywordsPolar Grassmann graph Apartment Isometric embedding Mathematics Subject Classification51A50 51E24 



Author: Mariusz Kwiatkowski - Mark Pankov

Source: https://link.springer.com/







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