Abstract
We characterize reflectable bases for affine reflection systems (extended affine root systems) of types This completes the characterization of reflectable bases for reduced affine reflections systems. We prove that a subset of non-isotropic roots is a reflectable base if and only if it is a minimal generating set for the root lattice. Our approach also provides a new less involved proof for simply laced types different from
Using our characterization, we enumerate reflectable bases for the finite type E6.
Acknowledgement
The first author would like to thank IPM-Isfahan Branch where this research was partially carried out there.