ON PLANARITY OF GRAPHS ON WEYL GROUPS

Authors

  • S. A. YOUSSEF Department of Mathematics, Indian Institute of Technology, Kharagpur-721 302, India.
  • S. G. HULSURKAR Department of Mathematics, Indian Institute of Technology, Kharagpur-721 302, India.

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4415

Keywords:

Weyl groups, root system, planarity of a graph

Abstract

A graph is constructed whose vertices are elements of a Weyl group and the edges are defined through nonvanishing of Wey!'s dimension polynomial at the point associated with two elements of the Weyl group. We study the planarity of such graphs on Weyl groups whose associated root system is irreducible. These graphs include four families of infinite number of graphs. We show that very few graphs, essentially five of them, are planar.

References

L. Chaskofsky, "Variation on Hulsurkar's matrix with applications to representation of algebraic Chevalley groups," J. Algebra, 82, 255-274, 1983.

F. Harary, Graph Theory, Addison Wesley. Mass., 1972.

S. G. Hulsurkar, "Proof of Verma's conjecture on Weyl's dimension polynomial," Inventiones Math., 27, 45-52, 1974.

J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1972.

Samy A. Youssef, Ph. D. Thesis, Indian Istitute of Technology, Kharagpur, July 1993.

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Published

1995-12-01

How to Cite

YOUSSEF, S. A., & HULSURKAR, S. G. (1995). ON PLANARITY OF GRAPHS ON WEYL GROUPS. Tamkang Journal of Mathematics, 26(4), 361–369. https://doi.org/10.5556/j.tkjm.26.1995.4415

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Section

Papers