We classify the reflectable bases of root systems of types , and . We give a graph-theoretical characterization of reflectable bases and count the number of reflectable bases for each type. We also give a Dynkin-type characterization of reflectable bases of root systems of types and .
Cite this article
Saeid Azam, Mohammad Bagher Soltani, Masaya Tomie, Yoji Yoshii, A Graph-Theoretical Classification for Reflectable Bases. Publ. Res. Inst. Math. Sci. 55 (2019), no. 4, pp. 689–736DOI 10.4171/PRIMS/55-4-2