A new Weyl group action and a cluster structure for representations of shifted quantum groups
アブストラクト
Shifted quantum affine algebras and their truncations emerged from the study of quantized Coulomb branches. I will report on a joint work with Geiss and Leclerc : we show that the Grothendieck ring of the category O for the shifted quantum affine algebras has the structure of a cluster algebra, with initial seeds parametrized by reduced expressions of the associated (finite) Weyl group W. The cluster variables of a class of distinguished initial seeds are certain formal power series defined from a Weyl group action introduced in a joint work with Frenkel.