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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.25243 |
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| _version_ | 1866915962599505920 |
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| author | Massicot, Valentin |
| author_facet | Massicot, Valentin |
| contents | Motivated by branching problems for principal series representations of the Lie group $G = GL(n,\mathbb R)$, we consider all pairs $(G', P)$ with $G'$ being the Levy factor of a parabolic subgroup of $G$ and $P$ a parabolic subgroup of $G$ for which a Borel subgroup $B'$ of $G'$ has finitely many orbits on $G/P$. We classify all such pairs $(G',P)$ for which $B'$-orbits on the generalized flag variety $G/P$ are determined by invariant functions inspired from the Bruhat decomposition. We also describe explicitly the double coset space $B'\backslash G/P$ as well as the closed $B'$-orbits on $G/P$ whenever $B'$-orbits are computed by these invariant functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $B'$-orbits on flag varieties and symmetry breaking Massicot, Valentin Representation Theory 22E45, 57S25, 14M15 Motivated by branching problems for principal series representations of the Lie group $G = GL(n,\mathbb R)$, we consider all pairs $(G', P)$ with $G'$ being the Levy factor of a parabolic subgroup of $G$ and $P$ a parabolic subgroup of $G$ for which a Borel subgroup $B'$ of $G'$ has finitely many orbits on $G/P$. We classify all such pairs $(G',P)$ for which $B'$-orbits on the generalized flag variety $G/P$ are determined by invariant functions inspired from the Bruhat decomposition. We also describe explicitly the double coset space $B'\backslash G/P$ as well as the closed $B'$-orbits on $G/P$ whenever $B'$-orbits are computed by these invariant functions. |
| title | $B'$-orbits on flag varieties and symmetry breaking |
| topic | Representation Theory 22E45, 57S25, 14M15 |
| url | https://arxiv.org/abs/2604.25243 |