Corpus ID: 14364517

A third look at weight diagrams

@article{Vavilov2000ATL,
  title={A third look at weight diagrams},
  author={N. Vavilov},
  journal={Rendiconti del Seminario Matematico della Universit{\`a} di Padova},
  year={2000},
  volume={104},
  pages={201-250}
}
  • N. Vavilov
  • Published 2000
  • Mathematics
  • Rendiconti del Seminario Matematico della Università di Padova
In this paper, which is a sequel of [PSV], we develop a completely elementary approach to calculations in Chevalley groups G = G(O, R) of types 0 = E6 and E7 over a commutative ring using only the weight diagrams (alias, crystal graphs) of their minimal modules. After an elementary construction of a crystal base we explicitly describe action of root subgroups and of the extended Weyl group, multilinear invariants, equations defining the orbit of the highest weight vector and Freudenthal… Expand

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