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 ${\frak g}$. Such total orders are called convex orders and are used to construct convex bases of PoincaréBirkhoffWitt type of the upper triangular subalgebra $U_q^+$ of the quantized enveloping algebra $U_q({\frak g})$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:math/9912020
 Bibcode:
 1999math.....12020I
 Keywords:

 Quantum Algebra;
 Representation Theory
 EPrint:
 30pages, AMSLaTeX