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Double flag varieties of Levi type with a finite number of orbits
Abstract
We consider a double flag variety of the form L/Q× G/P where G is a connected reductive group and L is a Levi subgroup of G. The Levi subgroup L acts diagonally on this double flag variety and a basic problem is to classify pairs of parabolic subgroups P⊂ G and Q⊂ L such that there are finitely many orbits for the considered action. We solve this problem in the case where G is the general linear group by using representations of quivers.
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BibTeX
@misc{fresse2026double,
title = {{Double flag varieties of Levi type with a finite number of orbits}},
author = {Lucas Fresse and Kyo Nishiyama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21092},
eprint = {2609.21092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21092},
}
RIS
TY - UNPB
TI - Double flag varieties of Levi type with a finite number of orbits
AU - Lucas Fresse
AU - Kyo Nishiyama
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21092
UR - https://arxiv.org/abs/2609.21092
AB - We consider a double flag variety of the form L/Q× G/P where G is a connected reductive group and L is a Levi subgroup of G. The Levi subgroup L acts diagonally on this double flag variety and a basic problem is to classify pairs of parabolic subgroups P⊂ G and Q⊂ L such that there are finitely many orbits for the considered action. We solve this problem in the case where G is the general linear group by using representations of quivers.
ER -