Geodesic
Lawrence–Krammer–Bigelow representations and dual Garside length of braids
Ito, Tetsuya1 ; Wiest, Bertold2
1 Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
2 IRMAR, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
Geometry & topology, Tome 19 (2015) no. 3, pp. 1361-1381.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that the span of the variable q in the Lawrence–Krammer–Bigelow representation matrix of a braid is equal to twice the dual Garside length of the braid, as was conjectured by Krammer. Our proof is close in spirit to Bigelow’s geometric approach. The key observation is that the dual Garside length of a braid can be read off a certain labeling of its curve diagram.

DOI : 10.2140/gt.2015.19.1361
Classification : 20F36, 20F10, 57M07
Keywords: Lawrence-Krammer-Bigelow representation, braid group, curve diagram, dual Garside length

Ito, Tetsuya 1 ; Wiest, Bertold 2

1 Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
2 IRMAR, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France 
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Ito, Tetsuya; Wiest, Bertold. Lawrence–Krammer–Bigelow representations and dual Garside length of braids. Geometry & topology, Tome 19 (2015) no. 3, pp. 1361-1381. doi : 10.2140/gt.2015.19.1361. http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.1361/

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