Differential contra algebraic invariants: Applications to classical algebraic problems
- Авторы: Bibikov P.1, Lychagin V.1
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Учреждения:
- Institute of Control Sciences
- Выпуск: Том 37, № 1 (2016)
- Страницы: 36-49
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197295
- DOI: https://doi.org/10.1134/S1995080216010030
- ID: 197295
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Аннотация
In this paper we discuss an approach to the study of orbits of actions of semisimple Lie groups in their irreducible complex representations,which is based on differential invariants on the one hand, and on geometry of reductive homogeneous spaces on the other hand. According to the Borel–Weil–Bott theorem, every irreducible representation of semisimple Lie group is isomorphic to the action of this group on the module of holomorphic sections of some one–dimensional bundle over homogeneous space. Using this, we give a complete description of the structure of the field of differential invariants for this action and obtain a criterion which separates regular orbits.
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Об авторах
P. Bibikov
Institute of Control Sciences
Автор, ответственный за переписку.
Email: tsdtp4u@proc.ru
Россия, Profsoyuznaya 65, Moscow, 117997
V. Lychagin
Institute of Control Sciences
Email: tsdtp4u@proc.ru
Россия, Profsoyuznaya 65, Moscow, 117997