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Theses

Correspondance de Satake géométrique, bases canoniques et involution de Schützenberger

Abstract : In this thesis we study geometric Satake correspondance. First we identify the intersection form throught the correspondance. It equals a contravariant form twisted by Schützenberger's involution. Then we use a combinatoric conjecture to demonstrate the compatibility of the Mirkovic and Vilonen basis with the Schützenberger involution. We demonstrate this conjecture for the sl2 case. The combinatoric tools created to demonstrate this conjecture allow us to demonstrate that the dual semicanonical basis semicanonique duale equals the generalized Mirovic et Vilonen basis.
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Arnaud Demarais. Correspondance de Satake géométrique, bases canoniques et involution de Schützenberger. Mathématiques générales [math.GM]. Université de Strasbourg, 2017. Français. ⟨NNT : 2017STRAD040⟩. ⟨tel-01652887v3⟩

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