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no. 6
Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups
Chapelier-Laget, Nathan1; Gobet, Thomas2
1 Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville Université du Littoral Côte d’Opale 50 rue Ferdinand Buisson CS 80699 62100 Calais
2 Laboratoire de Mathématiques Blaise Pascal CNRS UMR 6620 Université Clermont Auvergne Campus Universitaire des Cézeaux 3, place Vasarely TSA 60026 - CS 60026 63178 Aubière Cedex France
Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1751-1759.

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group W to cosets xW L θ , where x is an element of W and W L θ the subgroup of fixed points of an automorphism θ of order at most two of a standard parabolic subgroup W L of W. When θ≠id, there is in general more than one element of minimal length in a given coset, and we explain how to relate elements of minimal length. We also show that elements of minimal length in cosets are exactly those elements which are minimal for the restriction of the Bruhat order.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.394
Classification: 20F55
Mots-clés : Coxeter groups, Bruhat order

Chapelier-Laget, Nathan 1; Gobet, Thomas 2

1 Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville Université du Littoral Côte d’Opale 50 rue Ferdinand Buisson CS 80699 62100 Calais
2 Laboratoire de Mathématiques Blaise Pascal CNRS UMR 6620 Université Clermont Auvergne Campus Universitaire des Cézeaux 3, place Vasarely TSA 60026 - CS 60026 63178 Aubière Cedex France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chapelier-Laget, Nathan; Gobet, Thomas. Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups. Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1751-1759. doi : 10.5802/alco.394. https://alco.centre-mersenne.org/articles/10.5802/alco.394/

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