• Honam Mathematical Journal
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• v.35 no.1
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• pp.1-15
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• 2013

In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.427-436
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• 2011

In this paper, we first show that the pull-back morphism between two K-groups of the Steinberg varieties, obtained respectively from partial flag varieties and quiver varieties of type A, is a ring homomorphism with respect to the convolution product. Then, we prove that this ring homomorphism yields a property of compatibility between two certain convolution actions.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.347-353
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• 2011

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.