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Habilitation à diriger des recherches

Propriétés et combinatoire des bases de type canonique

Abstract : To study the representations of a complex connected semisimple algebraic group G, one usually chooses a Borel subgroup B in G and a maximal torus T contained in B. Given a representation of G on a vector space V, it is thus natural to look at the bases of V that are compatible with this choice of (B,T). Works by Zelevinsky, Berenstein, Lusztig and Kashiwara led to the notions of " canonical basis ", " good basis ", " perfect basis ", " string basis ", ... , and to the construction of such bases. The aim of this memoir is to provide a short introduction to this theory and to present some remarkable properties of these bases and of the combinatorics they define.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00705204
Contributor : Pierre Baumann <>
Submitted on : Tuesday, June 12, 2012 - 10:37:46 AM
Last modification on : Thursday, July 9, 2020 - 8:36:25 AM
Long-term archiving on: : Thursday, September 13, 2012 - 2:21:09 AM

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  • HAL Id : tel-00705204, version 1

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Pierre Baumann. Propriétés et combinatoire des bases de type canonique. Théorie des représentations [math.RT]. Université de Strasbourg, 2012. ⟨tel-00705204⟩

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