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Mirković, Ivan; Vybornov, Maxim; Krylov, Vasily
Advances in mathematics (New York. 1965), 10/2022, Letnik: 407Journal Article
In type A we find equivalences of geometries arising in three settings: Nakajima's (“framed”) quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are all given by explicit formulas. In particular, we embedd the framed quiver varieties into Beilinson-Drinfeld Grassmannians. This provides a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application we provide a geometric version of symmetric and skew (GL(m),GL(n)) dualities.
