Abstract
The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action.
Highlights
In studying finite-dimensional representations of Yangian algebras and quantum affine algebras, Drinfeld gave a new realization of the Drinfeld-Jimbo quantum enveloping algebras of the affine types
Drinfeld realization is a quantum analog of the loop algebra realization of the affine Kac-Moody Lie algebras and has played a pivotal role in later developments of quantum affine algebras and the quantum conformal field theory
The basic representations of quantum affine algebras were constructed based on Drinfeld realization [1, 2] and the quantum Knizhnik-Zamolodchikov equation [3] was formulated using this realization
Summary
In studying finite-dimensional representations of Yangian algebras and quantum affine algebras, Drinfeld gave a new realization of the Drinfeld-Jimbo quantum enveloping algebras of the affine types. By directly quantizing the classical isomorphism of the Kac realization to the affine Lie algebras, the first author later gave an elementary proof [9] of the Drinfeld automorphism using q-brackets starting from Drinfeld’s quantum loop algebras. In this elementary approach a general strategy and algorithm was formulated to prove the Serre relations. We prove the isomorphism of two forms of quantum affine algebras using our previous work on Drinfeld realization and q-bracket techniques
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