Vol. 5, No. 1, 2012

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Permutation notations for the exceptional Weyl group $F_4$

Patricia Cahn, Ruth Haas, Aloysius G. Helminck, Juan Li and Jeremy Schwartz

Vol. 5 (2012), No. 1, 81–89
Abstract

This paper describes a permutation notation for the Weyl groups of type ${F}_{4}$ and ${G}_{2}$. The image in the permutation group is presented as well as an analysis of the structure of the group. This description enables faster computations in these Weyl groups which will prove useful for a variety of applications.

Keywords
Weyl groups, Coxeter groups, one-line notation, permutations
Mathematical Subject Classification 2010
Primary: 20G15, 20G20, 22E15, 22E46, 43A85