Orbit duality in ind-varieties of maximal generalized flags
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- by Lucas Fresse and Ivan Penkov
- Trans. Moscow Math. Soc. 2017, 131-160
- DOI: https://doi.org/10.1090/mosc/266
- Published electronically: December 1, 2017
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Abstract:
We extend Matsuki duality to arbitrary ind-varieties of maximal generalized flags, in other words, to any homogeneous ind-variety $\mathbf {G}/\mathbf {B}$ for a classical ind-group $\mathbf {G}$ and a splitting Borel ind-subgroup $\mathbf {B}\subset \mathbf {G}$. As a first step, we present an explicit combinatorial version of Matsuki duality in the finite-dimensional case, involving an explicit parametrization of $K$- and $G^0$-orbits on $G/B$. After proving Matsuki duality in the infinite-dimensional case, we give necessary and sufficient conditions on a Borel ind-subgroup $\mathbf {B}\subset \mathbf {G}$ for the existence of open and closed $\mathbf {K}$- and $\mathbf {G}^0$-orbits on $\mathbf {G}/\mathbf {B}$, where $\left (\mathbf {K},\mathbf {G}^0\right )$ is an aligned pair of a symmetric ind-subgroup $\mathbf {K}$ and a real form $\mathbf {G}^0$ of $\mathbf {G}$.References
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Bibliographic Information
- Lucas Fresse
- Affiliation: Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506 France
- MR Author ID: 875745
- Email: lucas.fresse@univ-lorraine.fr
- Ivan Penkov
- Affiliation: Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
- Email: i.penkov@jacobs-university.de
- Published electronically: December 1, 2017
- Additional Notes: The first author was supported in part by ISF Grant Nr. 797/14 and by ANR project GeoLie (ANR-15-CE40-0012).
The second author was supported in part by DFG Grant PE 980/6-1. - © Copyright 2017 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2017, 131-160
- MSC (2010): Primary 14L30, 14M15, 22E65, 22F30
- DOI: https://doi.org/10.1090/mosc/266
- MathSciNet review: 3738082
Dedicated: To Ernest Borisovich Vinberg on the occasion of his 80th birthday