JournalsprimsVol. 55, No. 4pp. 689–736

A Graph-Theoretical Classification for Reflectable Bases

  • Saeid Azam

    University of Isfahan, Iran and Institute for Research in Fundamental Sciences, Tehran, Iran

  • Mohammad Bagher Soltani

    University of Isfahan, Iran

  • Masaya Tomie

    Morioka University, Takizawa, Japan

  • Yoji Yoshii

    Iwate University, Morioka, Japan
A Graph-Theoretical Classification for Reflectable Bases cover

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Abstract

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. 689–736

DOI 10.4171/PRIMS/55-4-2