Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

Ivan Mirković; Maxim Vybornov

Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

Algebraic Geometry 2008-12-31 v2 Representation Theory

Authors: Ivan Mirković , Maxim Vybornov

Abstract

We construct Nakajima's quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy's) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima's quiver varieties and a decomposition of an affine Grassmannian into a disjoint union of quiver varieties. As an application we provide a geometric version of skew and symmetric $(GL(m), GL(n))$ duality.

Keywords

quiver varieties beilinson-drinfeld grassmannians nakajima varieties affine grassmannians conjugacy classes transverse slices gl(m) gl(n) duality compactification

Cite

@article{arxiv.0712.4160,
  title  = {Quiver varieties and Beilinson-Drinfeld Grassmannians of type A},
  author = {Ivan Mirković and Maxim Vybornov},
  journal= {arXiv preprint arXiv:0712.4160},
  year   = {2008}
}

Comments

36 pages. Minor errors corrected on page 12, references added

Quiver varieties and Beilinson-Drinfeld Grassmannians of type A

Abstract

Keywords

Cite

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