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The closure ordering of adjoint nilpotent orbits in so(p,q)
http://hdl.handle.net/10097/00105831
http://hdl.handle.net/10097/001058319030e6e1-2acf-43ce-b586-1584b48d3932
| Item type | [ELS]紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2017-04-07 | |||||
| タイトル | ||||||
| タイトル | The closure ordering of adjoint nilpotent orbits in so(p,q) | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| アクセス権 | ||||||
| アクセス権 | metadata only access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
| 雑誌書誌ID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA00863953 | |||||
| 論文名よみ | ||||||
| タイトル | The closure ordering of adjoint nilpotent orbits in so(p,q) | |||||
| 著者 |
Djokovic, Dragomir Z.
× Djokovic, Dragomir Z.× Lemire, Nicole× Sekiguchi, Jiro |
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| 著者所属(英) | ||||||
| 言語 | en | |||||
| 値 | Department ofPure Mathematics, University of Waterloo | |||||
| 著者所属(英) | ||||||
| 言語 | en | |||||
| 値 | Department of Mathematics,University of Oregon | |||||
| 著者所属(英) | ||||||
| 言語 | en | |||||
| 値 | Department of Mathematics, Tokyo University ofAgriculture andTechnolog | |||||
| 抄録(英) | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Let ${\mathcal{O}}$ be a nilpotent orbit in ${\mathfrak{so}}(p,q)$ under the adjoint action of the full orthogonal group ${\rm{O}}(p,q)$. Then the closure of ${\mathcal{O}}$ (with respect to the Euclidean topology) is a union of ${\mathcal{O}}$ and some nilpotent ${\rm{O}}(p,q)$-orbits of smaller dimensions. In an earlier work, the first author has determined which nilpotent ${\rm{O}}(p,q)$-orbits belong to this closure. The same problem for the action of the identity component ${\rm{SO}}(p,q)^0$ of ${\rm{O}}(p,q)$ on ${\mathfrak{so}}(p,q)$ is much harder and we propose a conjecture describing the closures of the nilpotent ${\rm{SO}}(p,q)^0$-orbits. The conjecture is proved when $\min(p,q)\le7$. Our method is indirect because we use the Kostant-Sekiguchi correspondence to translate the problem to that of describing the closures of the unstable orbits for the action of the complex group ${\rm{SO}} p({\bf{C}})\times{\rm{SO}} q({\bf{C}})$ on the space $M_{p,q}$ of complex $p\times q$ matrices with the action given by $(a,b)\cdot x=axb^<-1>$. The fact that the Kostant--Sekiguchi correspondence preserves the closure relation has been proved recently by Barbasch and Sepanski. | |||||
| 書誌情報 |
東北數學雜誌. Second series en : Tohoku mathematical journal. Second series 巻 53, 号 3, p. 395-442, 発行日 2001-09-01 |
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| URL | ||||||
| 識別子 | J-STAGE | https://www.jstage.jst.go.jp/article/tmj/53/3/53_3_395/_article/-char/ja | |||||
| 識別子タイプ | URI | |||||
| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 00408735 | |||||
