SHEAF-THEORETIC APPROACH TO THE CONVOLUTION ALGEBRAS ON QUIVER VARIETIES

• Kwon, Namhee (Department of Mathematics, Daegu University)
• Accepted : 2013.01.01
• Published : 2013.03.25

Abstract

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.

References

1. A. Beilinson, A. Bernstein and P. Deligne, Faisceaux pervers, Asterisque 100 (1982).
2. A. Borel and J. Moore, Homology theory for locally compact spaces, Michigan Math. J. 7 (1960), 137-159. https://doi.org/10.1307/mmj/1028998385
3. N. Chriss and V. Ginzburg, Representation theory and complex geometry, Birkhauser, Boston, 1997.
4. W. Crawley-Boevey, Geometry of the moment map for representations of quivers, Compositio Math. 126 (2001), 257-293. https://doi.org/10.1023/A:1017558904030
5. V. G. Kac, Infinite dimensional Lie algebras, 3rd ed., Cambridge Univ. Press, Cambridge, 1990.
6. A. King, Moduli of representations of finite dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), 515-530. https://doi.org/10.1093/qmath/45.4.515
7. N. Kwon, Borel-Moore homology and K-theory on the Steinberg variety, Michigan Math. J. 58 (2009), 771-781. https://doi.org/10.1307/mmj/1260475700
8. G. Lusztig, On quiver varieties, Adv. in Math. 136 (1998), 141-182. https://doi.org/10.1006/aima.1998.1729
9. 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
10. H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560. https://doi.org/10.1215/S0012-7094-98-09120-7
11. P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute Lectures 51, Springer-Verlag, 1978.
12. D. Yamakawa, Geometry of multiplicative preprojective algebra, IMRP 2008 (2008), 77pp.