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Article: On Orbits in Double Flag Varieties for Symmetric Pairs
Title | On Orbits in Double Flag Varieties for Symmetric Pairs |
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Authors | |
Issue Date | 2013 |
Citation | Transformation Groups, 2013, v. 18, n. 4, p. 1091-1136 How to Cite? |
Abstract | Let G be a connected, simply connected semisimple algebraic group over the complex number field, and let K be the fixed point subgroup of an involutive automorphism of G so that (G, K) is a symmetric pair. We take parabolic subgroups P of G and Q of K, respectively, and consider the product of partial flag varieties G/P and K/Q with diagonal K-action, which we call a double flag variety for a symmetric pair. It is said to be of finite type if there are only finitely many K-orbits on it. In this paper, we give a parametrization of K-orbits on G/P × K/Q in terms of quotient spaces of unipotent groups without assuming the finiteness of orbits. If one of P ⊂ G or Q ⊂ K is a Borel subgroup, the finiteness of orbits is closely related to spherical actions. In such cases, we give a complete classification of double flag varieties of finite type, namely, we obtain classifications of K-spherical flag varieties G/P and G-spherical homogeneous spaces G/Q. © 2013 Springer Science+Business Media New York. |
Persistent Identifier | http://hdl.handle.net/10722/329294 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.844 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | He, Xuhua | - |
dc.contributor.author | Ochiai, Hiroyuki | - |
dc.contributor.author | Nishiyama, Kyo | - |
dc.contributor.author | Oshima, Yoshiki | - |
dc.date.accessioned | 2023-08-09T03:31:46Z | - |
dc.date.available | 2023-08-09T03:31:46Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Transformation Groups, 2013, v. 18, n. 4, p. 1091-1136 | - |
dc.identifier.issn | 1083-4362 | - |
dc.identifier.uri | http://hdl.handle.net/10722/329294 | - |
dc.description.abstract | Let G be a connected, simply connected semisimple algebraic group over the complex number field, and let K be the fixed point subgroup of an involutive automorphism of G so that (G, K) is a symmetric pair. We take parabolic subgroups P of G and Q of K, respectively, and consider the product of partial flag varieties G/P and K/Q with diagonal K-action, which we call a double flag variety for a symmetric pair. It is said to be of finite type if there are only finitely many K-orbits on it. In this paper, we give a parametrization of K-orbits on G/P × K/Q in terms of quotient spaces of unipotent groups without assuming the finiteness of orbits. If one of P ⊂ G or Q ⊂ K is a Borel subgroup, the finiteness of orbits is closely related to spherical actions. In such cases, we give a complete classification of double flag varieties of finite type, namely, we obtain classifications of K-spherical flag varieties G/P and G-spherical homogeneous spaces G/Q. © 2013 Springer Science+Business Media New York. | - |
dc.language | eng | - |
dc.relation.ispartof | Transformation Groups | - |
dc.title | On Orbits in Double Flag Varieties for Symmetric Pairs | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00031-013-9243-8 | - |
dc.identifier.scopus | eid_2-s2.0-84887625029 | - |
dc.identifier.volume | 18 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 1091 | - |
dc.identifier.epage | 1136 | - |
dc.identifier.eissn | 1531-586X | - |
dc.identifier.isi | WOS:000328622800006 | - |