Differential contra algebraic invariants: Applications to classical algebraic problems
| Autor: | P. Bibikov, Valentin Lychagin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
010308 nuclear & particles physics
General Mathematics 010102 general mathematics (g K)-module Reductive group 01 natural sciences Representation theory Algebra Representation theory of SU Differential invariant Symmetric space 0103 physical sciences Fundamental representation 0101 mathematics Differential algebraic geometry Mathematics |
| Zdroj: | Lobachevskii Journal of Mathematics. 37:36-49 |
| ISSN: | 1818-9962 1995-0802 |
| DOI: | 10.1134/s1995080216010030 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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