Quiver Varieties and Yangians

Michela Varagnolo (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We prove a conjecture of Nakajima (for type A the result was announced by Ginzburg- Vasserot) giving a geometric realization, via quiver varieties, of the Yangian of type ADE (and more in general of the Yangian associated to every symmetric Kac-Moody Lie algebra). As a corollary we get that tthe characters of the simple finite dimensional representations of the quantized affine algebra and that of the yangian coincide.

Domaines: Algèbres quantiques [math.QA]

Michela Varagnolo. Quiver Varieties and Yangians. Letters in Mathematical Physics, 2000, 53, pp.273-283. ⟨hal-00019703⟩