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Quiver varieties and finite dimensional representations of quantum affine algebras


Author: Hiraku Nakajima
Journal: J. Amer. Math. Soc. 14 (2001), 145-238
MSC (2000): Primary 17B37; Secondary 14D21, 14L30, 16G20, 33D80
DOI: https://doi.org/10.1090/S0894-0347-00-00353-2
Published electronically: October 2, 2000
MathSciNet review: 1808477
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Abstract:

We study finite dimensional representations of the quantum affine algebra ${\mathbf{U}}_q(\widehat{\mathfrak{g}})$ using geometry of quiver varieties introduced by the author.

As an application, we obtain character formulas expressed in terms of intersection cohomologies of quiver varieties.


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Additional Information

Hiraku Nakajima
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: nakajima@kusm.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0894-0347-00-00353-2
Received by editor(s): December 9, 1999
Received by editor(s) in revised form: July 10, 2000
Published electronically: October 2, 2000
Additional Notes: The author was supported by the Grant-in-aid for Scientific Research (No.11740011), the Ministry of Education, Japan, and National Science Foundation Grant #DMS 97-29992.
Article copyright: © Copyright 2000 American Mathematical Society

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