Drinfeld-Beck isomophism of quantum affine algebra
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introduction
- Understanding the isomorphism between Drinfeld realization to the Drinfeld and Jimbo presentation of affine quantum algebras stated by Drinfeld has important applications in the study of the representation theory of affine quantum algebras
- using this result the finite dimensional irreducible representations of affine quantum algebras are classified in [CP1], [CP2] and [CP3];
- a geometrical realization (through the quiver varieties) of finite dimensional representations is constructed in [N] for the untwisted simply laced cases
expositions
- Zhang, Drinfeld Realisation Of Quantum Affine Algebras
- Zhang, Drinfeld-Jimbo & Drinfeld Presentations Of Quantum Loop Algebra (Non Twisted)
articles
- Naihuan Jing, Honglian Zhang, Drinfeld realization of quantum twisted affine algebras via braid group, arXiv:1301.3550 [math.QA], January 16 2013, http://arxiv.org/abs/1301.3550
- Damiani, Ilaria. 2014. “From the Drinfeld Realization to the Drinfeld-Jimbo Presentation of Affine Quantum Algebras: The Injectivity.” arXiv:1407.0341 [math], July. http://arxiv.org/abs/1407.0341.
- Damiani, Ilaria. “Drinfeld Realization of Affine Quantum Algebras: The Relations.” arXiv:1406.6729 [math], June 25, 2014. http://arxiv.org/abs/1406.6729.
- Jing, Naihuan, and Ming Liu. “Isomorphism between Two Realizations of the Yangian \(Y(\mathfrak {so}_3)\).” Journal of Physics A: Mathematical and Theoretical 46, no. 7 (February 22, 2013): 075201. doi:10.1088/1751-8113/46/7/075201.
- Burban, Igor, and Olivier Schiffmann. “Two Descriptions of the Quantum Affine Algebra \(U_v(\hat{\mathfrak{sl}}_2)\) via Hall Algebra Approach.” arXiv:0903.4828 [math], March 27, 2009. http://arxiv.org/abs/0903.4828.
- Jing, Naihuan. “On Drinfeld Realization of Quantum Affine Algebras.” arXiv:q-alg/9610035, October 31, 1996. http://arxiv.org/abs/q-alg/9610035.
- Beck, Jonathan. 1994. “Braid Group Action and Quantum Affine Algebras.” Communications in Mathematical Physics 165 (3): 555–568. http://link.springer.com/article/10.1007%2FBF02099423
- Ding, Jintai, and Igor B. Frenkel. “Isomorphism of Two Realizations of Quantum Affine algebraU_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}}).” Communications in Mathematical Physics 156, no. 2 (September 1993): 277–300. doi:10.1007/BF02098484.