Let $\frak{g}$ be a ADE type simple lie algebra. There are (at least) two geometric ways to get highest weight irreducible representations of $\frak{g}$. One is by considering constructible functions on Nakajima varieties $\oplus_{v}(M(\mathcal{L}(v,w))\cap L(w))\cong V^\lambda$ and another one is by geometric Satake correspondence [Mirkovic-Vilonen] $IH^*(\overline{\text{Gr}^\lambda})\cong V^\lambda$. I heard that there is 'symplectic duality' connecting them. What is it exactly?
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2$\begingroup$ This answers the "reference request" tag, at least: front.math.ucdavis.edu/search?a=braden+proudfoot+webster . Ben Webster will probably point you to which of his talks people.virginia.edu/~btw4e/talks.html goes into most detail about the quiver/Yangian case. $\endgroup$– Allen KnutsonCommented Dec 7, 2016 at 13:00
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