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Register a new userThe usage of the representative of the nilpotent orbit in the Lie algebra sp2n to obtain some adjectives of the weighted Dynkin diagram
استخدام ممّثلِ المدارِ عديمِ القوى في جبر لي sp2n في استكشافِ بعض سمات مخطَّط دينكن الموزون
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في هذه الورقة العلمية، صممت خوارزمية لاختبار هل كان مخطَّط دينكن الموزون من النمط -Cn مقابلاً لأحد مدارات sp2n عديمة القوى؟ و تعيين ممّثل هذا المدار، و من ثم تحديد الشَّرط اللازم و الكافي على هذا الممثل لكي يكون المخطَّط زوجياً. فضلاً عن ذلك، طُبقت هذه الخوارزمية على أحد مخطَّطات دينكن الموزونة من النمط –C3 للتحقُّق من صحتها.
In this scientific paper, we describe an algorithm to test if the weighted Dynkin diagram of type -Cn corresponds to one of the nilpotent orbits of sp2n, then we defined the necessary and sufficient condition on this representative that makes the diagram even. We applied this algorithm on one of the weighted Dynkin diagrams of type –C3 to prove that it is true
References used
Collingwood, D.H. and Mcgovern W.M, 1993. Nilpotent orbit in semisimple Lie algebras, Van Nostrand Reinhold, New York. pp 30, 70, 81, 82
Eradman, K. and Wildon, M.J., 2006. Introduction to Lie algebras, Springer Verlag, London. pp 1, 26, 30, 32, 54, 134, 135, 136
Panyushev, D. 1999. On spherical nilpotent orbits and beyond. Annales de l'institute Fourier, Grenoble, 49, 5, pp1453, 1476
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