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REMARKS ON THE MAFFEI'S ISOMORPHISM

  • Received : 2011.06.15
  • Accepted : 2011.08.02
  • Published : 2011.09.25

Abstract

In [1], Maffei proved a certain relationship between quiver varieties of type A and the geometry of partial flag varieties over the nilpotent cone. This relation was conjectured by Naka-jima, and Nakajima proved his conjecture for a simple case. In the Maffei's proof, the key step was a reduction of the general case of the conjecture to the simple case treated by Nakajima through a certain isomorphism. In this paper, we study properties of this isomorphism.

Keywords

Quiver varieties;group actions;Maffei's isomorphisms

References

  1. A. Maffei, Quiver varieties of type A, Comment. Math. Helv. 80 (2005), 1-27.
  2. H. Nakajima, Instantons on ALE spaces, quiver varieties and Kac-Moody algebras, Duke Math. J. 76 (1994), 365-416. https://doi.org/10.1215/S0012-7094-94-07613-8
  3. H. Nakajima, Quiver varieties and finite dimensional representations of quantum affine algebras, J. Amer. Math. Soc. 14 (2001), 145-238. https://doi.org/10.1090/S0894-0347-00-00353-2