Convex Bases of PBW type for Quantum Affine Algebras

Abstract

This note has two purposes. First we establish that the map defined in [L, $\S 40.2.5$ (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to a convex basis of Poincaré--Birkhoff--Witt (PBW) type for $\bup$, an affine untwisted quantized enveloping algebra of Drinfel${}^{\prime }$d and Jimbo. The computations in this paper are made possible by extending the usual braid group action by certain outer automorphisms of the algebra.

arXiv comment7 pages, to appear in Comm. Math. Phys

References in corpus (1)

• Braid Group Action and Quantum Affine Algebras

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