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

Abstract

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.

Date
Dec 15, 2020
Location
CIRM - BBB
Luminy, France
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Léa Bittmann
Research Associate