32 citations · 78 across the 5 of their papers we have counts for
6 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…
Quiver varieties and t-analogs of q-characters of quantum affine algebras
Hiraku Nakajima
Let us consider a specialization of an untwisted quantum affine algebra of type at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of…
Quiver varieties and finite dimensional representations of quantum affine algebras
Hiraku Nakajima
We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formu…