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The classification of convex orders on affine root systems

Ken Ito
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Abstract

We classify all total orders having a certain convex property on the positive root system of an arbitrary untwisted affine Lie algebra ${\frak g}$. Such total orders are called convex orders and are used to construct convex bases of Poincaré-Birkhoff-Witt type of the upper triangular subalgebra $U_q^+$ of the quantized enveloping algebra $U_q({\frak g})$.

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Ken Ito. 2000-05-26. The classification of convex orders on affine root systems. https://arxiv.org/abs/math/9912020

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