[Irréductibilité de la représentation de Lawrence–Krammer de l'algèbre BMW de type ]
La représentation de Lawrence–Krammer, introduite par Lawrence et Krammer pour montrer la linéarité du groupe de tresses, est génériquement irréductible. On montre ce fait et on montre également que lorsque les deux paramètres de la représentation prennent certaines valeurs complexes, la représentation devient réductible. On donne ici toutes les valeurs des paramètres pour lesquelles la représentation est réductible, ainsi que les dimensions des sous-espaces stables.
The Lawrence–Krammer representation introduced by Lawrence and Krammer in order to show the linearity of the braid group is generically irreducible. We show this fact and show further that for some values of its two parameters, when these are specialized to complex numbers, the representation becomes reducible. We describe what these values are and give a complete description of the dimensions of the invariant subspaces when the representation is reducible.
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author = {Levaillant, Claire},
title = {Irreducibility of the {Lawrence{\textendash}Krammer} representation of the {BMW} algebra of type $ {A}_{n-1}$},
journal = {Comptes Rendus. Math\'ematique},
pages = {15--20},
publisher = {Elsevier},
volume = {347},
number = {1-2},
year = {2009},
doi = {10.1016/j.crma.2008.11.011},
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Levaillant, Claire. Irreducibility of the Lawrence–Krammer representation of the BMW algebra of type $ {A}_{n-1}$. Comptes Rendus. Mathématique, Tome 347 (2009) no. 1-2, pp. 15-20. doi : 10.1016/j.crma.2008.11.011. http://www.numdam.org/articles/10.1016/j.crma.2008.11.011/
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☆ This work is part of the author's PhD thesis at Caltech under the direction of Professor David B. Wales.
