Abstract
We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions.
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The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2013R1A1A2012783). The second author is supported by NSFC (Project No. 11401489), and the third author is supported by NCET-13-0396 and NSFC (Project No. 11271268).
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Lee, JH., Xu, M. & Zhang, J. Polytopes, quasi-minuscule representations and rational surfaces. Czech Math J 67, 397–415 (2017). https://doi.org/10.21136/CMJ.2017.0676-15
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DOI: https://doi.org/10.21136/CMJ.2017.0676-15