We study finite-dimensional representations of current algebras, loop algebras and their
quantized versions. For the current algebra of a simple Lie algebra of type ADE, we show …

Global and local Weyl modules were introduced via generators and relations in the context
of affine Lie algebras in [CP2] and were motivated by representations of quantum affine …

Each integrable lowest weight representation of a symmetrizable Kac-Moody Lie algebra g
has a crystal in the sense of Kashiwara, which describes its combinatorial properties. For a …

We prove the Kirillov–Reshetikhin (KR) conjecture in the general case: for all twisted
quantum affine algebras, we prove that the characters of KR modules solve the twisted Q …

Using the methods of Kang et al. and recent results on the characters of Kirillov–Reshetikhin
modules by Nakajima and Hernandez, the existence of Kirillov–Reshetikhin crystals $ B^{r …

In this paper, we introduce a family of indecomposable finite-dimensional graded modules
for the current algebra associated to a simple Lie algebra. These modules are indexed by …

We describe how Mirković–Vilonen (MV) polytopes arise naturally from the categorification
of Lie algebras using Khovanov–Lauda–Rouquier (KLR) algebras. This gives an explicit …

In this survey, we shall be concerned with the category of finite–dimensional representations
of the untwisted quantum affine algebra when the quantum parameter q is not a root of unity …

We establish the equality of the specialization E wλ (x; q; 0) of the nonsymmetric Macdonald
polynomial E wλ (x; q; t) at t= 0 with the graded character gch U w+(λ) of a certain Demazure …

Simple tensor products Page 1 Invent math (2010) 181: 649–675 DOI 10.1007/s00222-010-0256-9
Simple tensor products David Hernandez Received: 4 July 2009 / Accepted: 7 May 2010 …