Séminaires : Séminaire d'Algèbre

This is a report on an ongoing joint project with David Hernandez (Université Paris Cité) and Bernard Leclerc (Université de Caen). We define for each Cartan matrix of finite type a skew symmetric cluster algebra A of infinite rank in terms of an almost periodic quiver. By choosing an initial seed, where the cluster variables are certain formal power series, which fulfill the q-difference equations of a QQ-system, we can identify an adequate completion of A with the Grothendieck ring of the category O_Z of the corresponding (untwisted) shifted quantum affine algebras. We conjecture that under this identification the cluster monomials become the q-characters of the real simple representations in this category. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.