Théo Pinet
McGill University
Title
Generalized prefundamentals and cluster algebras
Abstract
Shifted Yangians are infinite-dimensional algebras of capital importance in the study of integrable systems, Coulomb branches and cluster categorifications. They admit remarkable quotients, called truncations, which are (graded) quantizations of generalized slices in affine grassmannians.
In this talk, we show that a notable family of representations for the truncations, the “generalized prefundamental modules”, satisfy the so-called “extended QQ-relations”. This proves a conjecture of Frenkel—Hernandez. We then explain how our results relate to the study of a cluster algebra that was recently introduced by Geiss—Hernandez—Leclerc.
This is based on joint work with Artem Kalmykov, Joel Kamnitzer, Alexis Leroux-Lapierre and Alex Weekes.
