Beyond Kirillov-Reshetikhin modules

Vyjayanthi Chari , David Hernandez (1, 2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 DMA - Département de Mathématiques et Applications - ENS Paris

In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review the foundational results of the subject, including the Drinfeld presentation, the classification of simple representations and q-characters. We then concentrate on particular families of irreducible representations whose structure has recently been understood: Kirillov-Reshetikhin modules, minimal affinizations and beyond.

Domaines: Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]

Vyjayanthi Chari, David Hernandez. Beyond Kirillov-Reshetikhin modules. 2008. ⟨hal-00345789⟩