The classification of convex orders on affine root systems
Abstract
We classify all total orders having a certain convex property on the positive root system of an arbitrary untwisted affine Lie algebra g. Such total orders are called convex orders and are used to construct convex bases of Poincar\'e-Birkhoff-Witt type of the upper triangular subalgebra Uq+ of the quantized enveloping algebra Uq( g).
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