Involve: A Journal of Mathematics

  • Involve
  • Volume 5, Number 1 (2012), 81-89.

Permutation notations for the exceptional Weyl group $F_4$

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

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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.

Article information

Involve, Volume 5, Number 1 (2012), 81-89.

Received: 25 June 2011
Revised: 22 August 2011
Accepted: 28 August 2011
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 20G15: Linear algebraic groups over arbitrary fields 20G20: Linear algebraic groups over the reals, the complexes, the quaternions 22E15: General properties and structure of real Lie groups 22E46: Semisimple Lie groups and their representations 43A85: Analysis on homogeneous spaces

Weyl groups Coxeter groups one-line notation permutations


Cahn, Patricia; Haas, Ruth; Helminck, Aloysius; Li, Juan; Schwartz, Jeremy. Permutation notations for the exceptional Weyl group $F_4$. Involve 5 (2012), no. 1, 81--89. doi:10.2140/involve.2012.5.81.

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