Normality and smoothness of simple linear group compactifications
Identifieur interne : 000161 ( Main/Exploration ); précédent : 000160; suivant : 000162Normality and smoothness of simple linear group compactifications
Auteurs : Jacopo Gandini [Italie] ; Alessandro Ruzzi [France]Source :
- Mathematische Zeitschrift [ 0025-5874 ] ; 2013-10-01.
Abstract
Abstract: Given a semisimple algebraic group $$G$$ , we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant $$G\times G$$ -compactifications possessing a unique closed orbit which arise in a projective space of the shape $$\mathbb{P }(\mathrm{End}(V))$$ , where $$V$$ is a finite dimensional rational $$G$$ -module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of $$V$$ . In particular, we show that $${\mathrm{Sp}}(2r)$$ (with $$r \geqslant 1$$ ) is the unique non-adjoint simple group which admits a simple smooth compactification.
Url:
DOI: 10.1007/s00209-012-1136-3
Affiliations:
- France, Italie
- Auvergne (région administrative), Auvergne-Rhône-Alpes, Latium
- Clermont-Ferrand, Rome
- Université Blaise-Pascal
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Z.</title><idno type="ISSN">0025-5874</idno><idno type="eISSN">1432-1823</idno><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2013-10-01">2013-10-01</date><biblScope unit="volume">275</biblScope><biblScope unit="issue">1-2</biblScope><biblScope unit="page" from="307">307</biblScope><biblScope unit="page" to="329">329</biblScope></imprint><idno type="ISSN">0025-5874</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5874</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Given a semisimple algebraic group $$G$$ , we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant $$G\times G$$ -compactifications possessing a unique closed orbit which arise in a projective space of the shape $$\mathbb{P }(\mathrm{End}(V))$$ , where $$V$$ is a finite dimensional rational $$G$$ -module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of $$V$$ . In particular, we show that $${\mathrm{Sp}}(2r)$$ (with $$r \geqslant 1$$ ) is the unique non-adjoint simple group which admits a simple smooth compactification.</div></front></TEI><affiliations><list><country><li>France</li><li>Italie</li></country><region><li>Auvergne (région administrative)</li><li>Auvergne-Rhône-Alpes</li><li>Latium</li></region><settlement><li>Clermont-Ferrand</li><li>Rome</li></settlement><orgName><li>Université Blaise-Pascal</li></orgName></list><tree><country name="Italie"><region name="Latium"><name sortKey="Gandini, Jacopo" sort="Gandini, Jacopo" uniqKey="Gandini J" first="Jacopo" last="Gandini">Jacopo Gandini</name></region><name sortKey="Gandini, Jacopo" sort="Gandini, Jacopo" uniqKey="Gandini J" first="Jacopo" last="Gandini">Jacopo Gandini</name></country><country name="France"><region name="Auvergne-Rhône-Alpes"><name sortKey="Ruzzi, Alessandro" sort="Ruzzi, Alessandro" uniqKey="Ruzzi A" first="Alessandro" last="Ruzzi">Alessandro Ruzzi</name></region><name sortKey="Ruzzi, Alessandro" sort="Ruzzi, Alessandro" uniqKey="Ruzzi A" first="Alessandro" last="Ruzzi">Alessandro Ruzzi</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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