Séminaires : Séminaire Groupes, Représentations et Géométrie

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The talk is based on joint work with Arnaud Eteve.
We present a monoidal equivalence—universal Koszul duality—between genuine equivariant K-motives on Kac-Moody flag varieties and constructible monodromic sheaves on their Langlands duals.
Our framework unifies several known dualities, including Beilinson-Ginzburg-Soergel's Koszul duality and descriptions of monodromic sheaves on flag varieties. 
For affine Kac-Moody groups, we gain new insights into a conjectured quantum K-theoretic Satake equivalence. 
Moreover, the results are closely related to the potent categorical representations as recently proposed by Ben-Zvi and Nadler. 
The talk will also briefly address foundations on six functors for reduced K-motives and constructible monodromic sheaves.