Characterization and enumeration of reflectable bases of types

Abstract

We characterize reflectable bases for affine reflection systems (extended affine root systems) of types (Formula presented.) 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 (Formula presented.) Using our characterization, we enumerate reflectable bases for the finite type E 6. © 2022 Taylor & Francis Group, LLC.