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

This paper describes a permutation notation for the Weyl groups of type F4 and G2. 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.

Weyl groups, Coxeter groups, one-line notation, permutations
Mathematical Subject Classification 2010
Primary: 20G15, 20G20, 22E15, 22E46, 43A85
Received: 25 June 2011
Revised: 22 August 2011
Accepted: 28 August 2011
Published: 28 April 2012

Communicated by Joseph Gallian
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