Abstract
The characters of simple Lie algebras are naturally decomposed into lattice-polytope sums. The Brion formula for those polytope sums is remarkably similar to the Weyl character formula. Here we start to investigate if other character formulas have analogs for lattice-polytope sums, by focusing on the Demazure character formulas. Using Demazure operators, we write expressions for the lattice sums of the weight polytopes of rank-2 simple Lie algebras, and the rank-3 algebra A 3.
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Notes
- 1.
This question was already asked in [15].
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Acknowledgements
I thank Jørgen Rasmussen for collaboration and Chad Povey for 3D-printing rank-3 weight polytopes. This research was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Walton, M.A. (2021). Demazure Formulas for Weight Polytopes. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_27
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