Monoidal categorification of cluster algebra and quantum affine Schur-Weyl duality


The notion of monoidal categorification of cluster algebras was introduced by Hernandez and Leclerc in 2010, it consists in realizing the cluster algebra as the Grothendieck ring of a certain monoidal category of representation. The main example we will be interested in was introduced by the same authors, who conjectured that a category of finite-dimensional representations of a quantum affine algebra was a monoidal categorification of a cluster algebra. In type A, from the quantum affine Schur-Weyl duality, established by Chari and Pressley in 1996, this category is equivalent to a category of representations of general p-adic groups. We will see how this quantum affine Schur-Weyl duality can be used to transfer results from the p-adic setting to the quantum group setting, in the context of the aforementioned monoidal categorification conjecture.

Dec 15, 2020
Luminy, France
Léa Bittmann
Research Associate