Non symmetric quantum loop groups and critical convolution algebras
Résumé
We realize the quantum loop groups and shifted quantum loop groups of arbitrary types, possibly non symmetric, via the K-theoretical critical convolution algebras introduced by Varagnolo-Vasserot. This yields a generalization of Nakajima's construction of symmetric quantum loop groups via quiver varieties to non symmetric types. We also construct some simple modules, in particular all Kirillov-Reshethikin modules, using critical K-theory.