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Article: On intersections of conjugacy classes and bruhat cells

TitleOn intersections of conjugacy classes and bruhat cells
Authors
Issue Date2010
PublisherBirkhaeuser Boston. The Journal's web site is located at http://link.springer.de/link/service/journals/00031/
Citation
Transformation Groups, 2010, v. 15 n. 2, p. 243-260 How to Cite?
AbstractFor a connected semisimple algebraic group G over an algebraically closed field k and a fixed pair (B, B-) of opposite Borel subgroups of G, we determine when the intersection of a conjugacy class C in G and a double coset BwB- is nonempty, where w is in the Weyl group W of G. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on W and an involution mC ∈ W associated to C. We prove that the element mC is the unique maximal length element in its conjugacy class in W, and we classify all such elements in W. For G = SL(n + 1; k), we describe mC explicitly for every conjugacy class C, and when w ∈ W ≊ Sn+1 is an involution, we give an explicit answer to when C ∩ (BwB) is nonempty. © 2010 Springer Science+Business Media, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/124811
ISSN
2015 Impact Factor: 0.662
2015 SCImago Journal Rankings: 1.271
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChan, KYen_HK
dc.contributor.authorLu, JHen_HK
dc.contributor.authorTo, SKMen_HK
dc.date.accessioned2010-10-31T10:55:29Z-
dc.date.available2010-10-31T10:55:29Z-
dc.date.issued2010en_HK
dc.identifier.citationTransformation Groups, 2010, v. 15 n. 2, p. 243-260en_HK
dc.identifier.issn1083-4362en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124811-
dc.description.abstractFor a connected semisimple algebraic group G over an algebraically closed field k and a fixed pair (B, B-) of opposite Borel subgroups of G, we determine when the intersection of a conjugacy class C in G and a double coset BwB- is nonempty, where w is in the Weyl group W of G. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on W and an involution mC ∈ W associated to C. We prove that the element mC is the unique maximal length element in its conjugacy class in W, and we classify all such elements in W. For G = SL(n + 1; k), we describe mC explicitly for every conjugacy class C, and when w ∈ W ≊ Sn+1 is an involution, we give an explicit answer to when C ∩ (BwB) is nonempty. © 2010 Springer Science+Business Media, LLC.en_HK
dc.languageengen_HK
dc.publisherBirkhaeuser Boston. The Journal's web site is located at http://link.springer.de/link/service/journals/00031/en_HK
dc.relation.ispartofTransformation Groupsen_HK
dc.titleOn intersections of conjugacy classes and bruhat cellsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1083-4362&volume=15, No. 2&spage=243 &epage= 260&date=2010&atitle=On+intersections+of+conjugacy+classes+and+bruhat+cellsen_HK
dc.identifier.emailLu, JH:jhluhku@hku.hken_HK
dc.identifier.authorityLu, JH=rp00753en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00031-010-9084-7en_HK
dc.identifier.scopuseid_2-s2.0-77953959076en_HK
dc.identifier.hkuros182337en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77953959076&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume15en_HK
dc.identifier.issue2en_HK
dc.identifier.spage243en_HK
dc.identifier.epage260en_HK
dc.identifier.eissn1531-586X-
dc.identifier.isiWOS:000278968200001-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChan, KY=35789773100en_HK
dc.identifier.scopusauthoridLu, JH=35790078400en_HK
dc.identifier.scopusauthoridTo, SKM=36141388100en_HK
dc.identifier.citeulike7043064-

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