Abstract

We characterize shadows of residues in building shadow spaces by local properties. The results are applied to buildings with diagram ${\mathsf{Y}}_{l,m,n}$ (including ${\mathsf{E}}_k$, $k\in \left\{6,7,8\right\}$, and ${\mathsf{D}}_k$) to show that every subspace isomorphic to the shadow of a residue is the shadow of a residue.

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Mathematical Subject Classification 2010

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