Quiver varieties and Yangians (Q5930240)

Let \(Y_h(L g)\) be the Yangian associated to a simple Lie algebra \(g\) of type \(A, D, E\), associated to a Cartan matrix \((a_{ij})_{i, j\in I}\). The author constructs an algebra homomorphism \(\Phi_w: Y_h(L g) \to H^{G_w}(Z(w)\), for any \(w\in {\mathbb{N}} [I]\). Here \(Z(w)\) is some quiver variety, \(G_w\) is a naturally related algebraic group, and \(H^{G_w}\) stands for \(G_w\)-equivariant complex Borel-Moore cohomology. This result answers positively a conjecture of Nakajima [see \textit{H. Nakajima}, J. Am. Math. Soc. 14, No. 1, 145-238 (2001; Zbl 0981.17016)]; for type \(A_n\), the result was announced in [\textit{V. Ginzburg} and \textit{E. Vasserot}, Int. Math. Res. Not. 1993, No. 3, 67-85 (1993; Zbl 0785.17014)].