Littelmann path model: Difference between revisions

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* ''s''<sub>α</sub> [π]= ''e''<sub>α</sub><sup> – ''k''</sup> [π] if ''k'' > 0.
 
If π is a path lying wholly inside the positive Weyl chamber, the '''Littelmann graph''' <math>\mathcal{G}_\pi</math> is defined to be the coloured, directed graph having as vertices the non-zero paths obtained by successivlysuccessively applying the operators ''f''<sub>α</sub> to π. There is a directed arrow from one path to another labelled by the simple root α, if the target path is obtained from the source path by applying ''f''<sub>α</sub>.
* The Littelmann graphs of two paths are isomorphic as coloured, directed graphs if and only if the paths have the same end point.