Séminaire de Physique Mathématique

Symmetries of Convolution Categories and the Quantum Ngo Action

by Prof. Sam Gunningham (Edinburgh University)

Amphithéâtre Léon Motchane (I.H.E.S.)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

I will describe a remarkable symmetric monoidal category associated to a reductive group G, which acts centrally on any G-category. This construction quantizes the universal centralizer group scheme, together with its action on Hamiltonian G-spaces used by Ngo in his proof of the Fundamental Lemma. The category and its central action appear most naturally in a Langlands dual incarnation, which is phrased in terms of convolution on the affine Grassmannian, via work of Bezrukavnikov, Finkelberg and Mirkovic. This is joint work with David Ben-Zvi.

Organized by

Vasily Pestun & Chris Elliott