Geodesic
Reduced and Nonreduced Presentations of Weyl Group Elements
Sven Balnojan1 ; Claus Hertling1
1Lehrstuhl für Mathematik VI, Universität Mannheim, 68131 Mannheim, Germany
Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 559-599

Voir la notice de l'article provenant de la source Heldermann Verlag

This paper is a sequel to work of E. B. Dynkin [Semisimple subalgebras of semisimple Lie algebras, Translations of the AMS (2) 6 (1957) 111--244] on subroot lattices of root lattices and to work of R. W. Carter [Conjugacy classes in the Weyl group, Comp. Math. 25 (1972) 1--59] on presentations of Weyl group elements as products of reflections.
The quotients L/L1 are calculated for all irreducible root lattices L and all subroot lattices L1. The reduced (i.e. those with minimal number of reflections) presentations of Weyl group elements as products of arbitrary reflections are classified. Also nonreduced presentations are studied. Quasi-Coxeter elements and strict quasi-Coxeter elements are defined and classified. An application to extended affine root lattices is given. A side result is that any set of roots which generates the root lattice contains a Z-basis of the root lattice.
Classification : 17B22, 20F55
Mots-clés : Root system, subroot lattice, reduced presentation, quasi-Coxeter element, extended affine root system

Sven Balnojan  1   ; Claus Hertling  1

1 Lehrstuhl für Mathematik VI, Universität Mannheim, 68131 Mannheim, Germany 
Sven Balnojan; Claus Hertling. Reduced and Nonreduced Presentations of Weyl Group Elements. Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 559-599. http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a10/
@article{JOLT_2019_29_2_a10,
     author = {Sven Balnojan and Claus Hertling},
     title = {Reduced and {Nonreduced} {Presentations} of {Weyl} {Group} {Elements}},
     journal = {Journal of Lie Theory},
     pages = {559--599},
     year = {2019},
     volume = {29},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a10/}
}
TY  - JOUR
AU  - Sven Balnojan
AU  - Claus Hertling
TI  - Reduced and Nonreduced Presentations of Weyl Group Elements
JO  - Journal of Lie Theory
PY  - 2019
SP  - 559
EP  - 599
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a10/
ID  - JOLT_2019_29_2_a10
ER  - 
%0 Journal Article
%A Sven Balnojan
%A Claus Hertling
%T Reduced and Nonreduced Presentations of Weyl Group Elements
%J Journal of Lie Theory
%D 2019
%P 559-599
%V 29
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a10/
%F JOLT_2019_29_2_a10