#### 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
##### Milestones
Received: 25 June 2011
Revised: 22 August 2011
Accepted: 28 August 2011
Published: 28 April 2012

Communicated by Joseph Gallian
##### Authors
 Patricia Cahn Department of Mathematics Dartmouth College Hanover, NH 03755 United States Ruth Haas Department of Mathematics and Statistics Smith College Northampton, MA 01063 United States Aloysius G. Helminck Department of Mathematics North Carolina State University Raleigh, NC 27695 United States Juan Li School of Operations Research and Information Engineering Cornell University Ithaca, NY 14850 United States Jeremy Schwartz Department of Mathematics University of Maryland College Park, MD 20742 United States