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Article Dans Une Revue Journal of the European Mathematical Society Année : 2022

Bases of tensor products and geometric Satake correspondence

Résumé

The geometric Satake correspondence can be regarded as a geometric construction of the rational representations of a complex connected reductive group G. In their study of this correspondence, Mirković and Vilonen introduced algebraic cycles that provide a linear basis in each irreducible representation. Generalizing this construction, Goncharov and Shen define a linear basis in each tensor product of irreducible representations. We investigate these bases and show that they share many properties with the dual canonical bases of Lusztig.
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hal-02928298 , version 1 (29-05-2024)

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Pierre Baumann, Stéphane Gaussent, Peter Littelmann. Bases of tensor products and geometric Satake correspondence. Journal of the European Mathematical Society, 2022, 26 (3), pp.919-983. ⟨10.4171/JEMS/1302⟩. ⟨hal-02928298⟩
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