[Geometrical lifting of the canonical base and Schützenberger involution]
Let G be a complex simply connected semisimple Lie group, and let be the canonical base of a Weyl module V of G. We calculate explicitely the action of the longest element w0 of the Weyl group on in terms of parametrizations. The method is based on results of Berenstein and Zelevinski (Invent. Math. 82 (2001) 77–128) on the geometric lifting.
Soit G un groupe de Lie complexe semisimple simplement connexe, et la base canonique d'un module de Weyl V de G. On calcule explicitement en terme de paramétrisation l'action du plus long élément du groupe de Weyl sur . On utilise pour cela les résultats de Berenstein et Zelevinski (Invent. Math. 82 (2001) 77–128) sur le relèvement géométrique.
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Sophie Morier-Genoud 1
@article{CRMATH_2003__337_6_371_0, author = {Sophie Morier-Genoud}, title = {Rel\`evement g\'eom\'etrique de la base canonique et involution de {Sch\"utzenberger}}, journal = {Comptes Rendus. Math\'ematique}, pages = {371--374}, publisher = {Elsevier}, volume = {337}, number = {6}, year = {2003}, doi = {10.1016/j.crma.2003.07.001}, language = {fr}, }
Sophie Morier-Genoud. Relèvement géométrique de la base canonique et involution de Schützenberger. Comptes Rendus. Mathématique, Volume 337 (2003) no. 6, pp. 371-374. doi : 10.1016/j.crma.2003.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.07.001/
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