Abstract
A symplectic polarity of a building {\Delta} of type E6 is a polarity whose fixed point structure is a building of type F4 containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type F4). In this paper, we show in a geometric way that every building of type E6 contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type F4 fully embedded in the natural point-line geometry of {\Delta} arises from a symplectic polarity.
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More From: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
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