Parabolic Actions in type A and their Eigenslices
Identifieur interne : 000956 ( Main/Curation ); précédent : 000955; suivant : 000957Parabolic Actions in type A and their Eigenslices
Auteurs : Anthony Joseph Joseph [Israël]Source :
- Transformation Groups [ 1083-4362 ] ; 2007-09-01.
Abstract
Abstract: The main theme of this paper is that many of the remarkable properties of invariant theory pertaining to semisimple Lie algebras carry over to parabolic subalgebras even though the latter have less structure. This includes the polynomiality of the invariant subalgebra of the symmetric algebra of a (truncated) parabolic subalgebra, the existence of a slice to the regular coadjoint orbits and the construction of maximal Poisson commutative polynomial subalgebras by "shift of argument". The first of these properties was established for most parabolics in [FJ1]. Here the existence of a slice to (most) regular coadjoint orbits is established for parabolics in type A which are invariant under the Dynkin diagram involution. In a subsequent paper [JL] maximal Poisson commutative polynomial subalgebras are described for those (truncated) parabolics in sl(n) having index n - 1.
Url:
DOI: 10.1007/s00031-006-0048-x
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :000948
- to stream Istex, to step Curation: Pour aller vers cette notice dans l'étape Curation :000948
- to stream Istex, to step Checkpoint: Pour aller vers cette notice dans l'étape Curation :000903
- to stream Main, to step Merge: Pour aller vers cette notice dans l'étape Curation :000963
Links to Exploration step
ISTEX:2CF5047739653DC2DD0A82FF65C2F259717E437DLe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Parabolic Actions in type A and their Eigenslices</title><author><name sortKey="Joseph, Anthony Joseph" sort="Joseph, Anthony Joseph" uniqKey="Joseph A" first="Anthony Joseph" last="Joseph">Anthony Joseph Joseph</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:2CF5047739653DC2DD0A82FF65C2F259717E437D</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/s00031-006-0048-x</idno><idno type="url">https://api.istex.fr/document/2CF5047739653DC2DD0A82FF65C2F259717E437D/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000948</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000948</idno><idno type="wicri:Area/Istex/Curation">000948</idno><idno type="wicri:Area/Istex/Checkpoint">000903</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000903</idno><idno type="wicri:doubleKey">1083-4362:2007:Joseph A:parabolic:actions:in</idno><idno type="wicri:Area/Main/Merge">000963</idno><idno type="wicri:Area/Main/Curation">000956</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Parabolic Actions in type A and their Eigenslices</title><author><name sortKey="Joseph, Anthony Joseph" sort="Joseph, Anthony Joseph" uniqKey="Joseph A" first="Anthony Joseph" last="Joseph">Anthony Joseph Joseph</name><affiliation wicri:level="1"><country xml:lang="fr">Israël</country><wicri:regionArea>Donald Frey, Professional Chair, Department of Mathematics, Weizmann Institute, Rehovot, 76100</wicri:regionArea><wicri:noRegion>76100</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Israël</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Transformation Groups</title><title level="j" type="abbrev">Transformation Groups</title><idno type="ISSN">1083-4362</idno><idno type="eISSN">1531-586X</idno><imprint><publisher>Birkhäuser-Verlag; www.birkhauser.com</publisher><pubPlace>Boston</pubPlace><date type="published" when="2007-09-01">2007-09-01</date><biblScope unit="volume">12</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="515">515</biblScope><biblScope unit="page" to="547">547</biblScope></imprint><idno type="ISSN">1083-4362</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1083-4362</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The main theme of this paper is that many of the remarkable properties of invariant theory pertaining to semisimple Lie algebras carry over to parabolic subalgebras even though the latter have less structure. This includes the polynomiality of the invariant subalgebra of the symmetric algebra of a (truncated) parabolic subalgebra, the existence of a slice to the regular coadjoint orbits and the construction of maximal Poisson commutative polynomial subalgebras by "shift of argument". The first of these properties was established for most parabolics in [FJ1]. Here the existence of a slice to (most) regular coadjoint orbits is established for parabolics in type A which are invariant under the Dynkin diagram involution. In a subsequent paper [JL] maximal Poisson commutative polynomial subalgebras are described for those (truncated) parabolics in sl(n) having index n - 1.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000956 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Curation/biblio.hfd -nk 000956 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Curation
|type= RBID
|clé= ISTEX:2CF5047739653DC2DD0A82FF65C2F259717E437D
|texte= Parabolic Actions in type A and their Eigenslices
}}
| This area was generated with Dilib version V0.6.33. |  |