The classification of convex orders on affine root systems

Details The classification of convex orders on affine root systems The classification of convex orders on affine root systems

1999-12-02

arxiv.org/abs/math/9912020v3

Mathematics

Quantum Algebra

30pages, AMS-LaTeX

Scientific paper

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
Poincar\'e-Birkhoff-Witt type of the upper triangular subalgebra $U_q^+$ of the
quantized enveloping algebra $U_q({\frak g})$.

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