Quiver varieties and quantum affine algebras. (English. Japanese original) Zbl 1246.17021
Sugaku Expo. 19, No. 1, 53-78 (2006); translation from Sūgaku 52, No. 4, 337-359 (2000).
This is mainly an introduction of expository nature to quiver varieties and their applications, however also new results relating quiver varieties to quantum enveloping algebras of affine Lie algebras and their finite-dimensional representations are presented. First the author explains the construction of algebras via convolution products and geometric constructions of quantized enveloping algebras due to Ringel and Lusztig. Then the definition of quiver varieties is given and their relations to (non-affine) quantum enveloping algebras is explained.
See also the author’s paper [J. Am. Math. Soc. 14, No. 1, 145–238 (2001; Zbl 0981.17016)].
See also the author’s paper [J. Am. Math. Soc. 14, No. 1, 145–238 (2001; Zbl 0981.17016)].
Reviewer: Olaf Ninnemann (Berlin)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 14L30 | Group actions on varieties or schemes (quotients) |
| 16G20 | Representations of quivers and partially ordered sets |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
