Overview on the theory of double flag varieties for symmetric pairs ...
arXiv, 2023
academicJournal
Zugriff:
Let $ G $ be a connected reductive algebraic group and its symmetric subgroup $ K $. The variety $ \dblFV = K/Q \times G/P $ is called a double flag variety, where $ Q $ and $ P $ are parabolic subgroups of $ K $ and $ G $ respectively. In this article, we make a survey on the theory of double flag varieties for a symmetric pair $ (G, K) $ and report entirely new results and theorems on this theory. Most important topic is the finiteness of $ K $-orbits on $ \dblFV $. We summarize the classification of $ \dblFV $ of finite type, which are scattered in the literatures. In some respects such classifications are complete, and in some cases not. In particular, we get a classification of double flag varieties of finite type when a symmetric pair is of type AIII, using the theorems of Homma who describes ``indecomposable'' objects of such double flag varieties. Together with these classifications, newly developed embedding theory provides double flag varieties of finite type, which are new. Other ingredients in ... : 70 pages ...
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Overview on the theory of double flag varieties for symmetric pairs ...
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Autor/in / Beteiligte Person: | Fresse, Lucas ; Nishiyama, Kyo |
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Veröffentlichung: | arXiv, 2023 |
Medientyp: | academicJournal |
DOI: | 10.48550/arxiv.2309.17085 |
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