A new description of convex bases of PBW type for untwisted quantum affine algebras (Q614515)

In this article the author gives a new description of convex bases of \(U^+\) for the quantum affine algebra \(U_q(\mathfrak{g})\), where \(\mathfrak{g}\) is an arbitrary untwisted affine Lie algebra. These convex bases are constructed using concrete methods of constructing all convex orders on the set of all positive roots developed in [\textit{K. Ito}, ``The classification of convex orders on affine root systems'', Commun. Algebra 29, No. 12, 5605--5630 (2001; Zbl 0989.17016)].