237 citations · 1.2k across the 58 of their papers we have counts for
5 papers · 1 filter
Crystal bases and two-sided cells of quantum affine algebras
Jonathan Beck, Hiraku Nakajima
Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We construct a basis of $\U^+$ whi…
Geometric construction of representations of affine algebras
Hiraku Nakajima
Let be a finite subgroup of $\SL_2(\C)$. We consider -fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of componen…
t-analogs of q-characters of Kirillov-Reshetikhin modules of quantm affine algebras
Hiraku Nakajima
We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra $\Ua$ when $\hat\g$ is an untwisted affine Lie algebr…
Extremal weight modules of quantum affine algebras
Hiraku Nakajima
Let $\ag$ be an affine Lie algebra, and let $\Ua$ be the quantum affine algebra introduced by Drinfeld and Jimbo. In [Kas94] Kashiwara introduced a $\Ua$-module , having a gl…
t-analogs of q-characters of quantum affine algebras of type ,
Hiraku Nakajima
We give a tableaux sum expression of --analog of --characters of finite dimensional representations (standard modules) of quantum affine algebras $\Ul$ when $\g$ is of type $…