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Article: On intersections of conjugacy classes and bruhat cells
Title | On intersections of conjugacy classes and bruhat cells |
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Authors | |
Issue Date | 2010 |
Publisher | Birkhaeuser 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? |
Abstract | For 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 Identifier | http://hdl.handle.net/10722/124811 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.844 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chan, KY | en_HK |
dc.contributor.author | Lu, JH | en_HK |
dc.contributor.author | To, SKM | en_HK |
dc.date.accessioned | 2010-10-31T10:55:29Z | - |
dc.date.available | 2010-10-31T10:55:29Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | Transformation Groups, 2010, v. 15 n. 2, p. 243-260 | en_HK |
dc.identifier.issn | 1083-4362 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/124811 | - |
dc.description.abstract | For 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.language | eng | en_HK |
dc.publisher | Birkhaeuser Boston. The Journal's web site is located at http://link.springer.de/link/service/journals/00031/ | en_HK |
dc.relation.ispartof | Transformation Groups | en_HK |
dc.title | On intersections of conjugacy classes and bruhat cells | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+cells | en_HK |
dc.identifier.email | Lu, JH:jhluhku@hku.hk | en_HK |
dc.identifier.authority | Lu, JH=rp00753 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00031-010-9084-7 | en_HK |
dc.identifier.scopus | eid_2-s2.0-77953959076 | en_HK |
dc.identifier.hkuros | 182337 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77953959076&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 15 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 243 | en_HK |
dc.identifier.epage | 260 | en_HK |
dc.identifier.eissn | 1531-586X | - |
dc.identifier.isi | WOS:000278968200001 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Chan, KY=35789773100 | en_HK |
dc.identifier.scopusauthorid | Lu, JH=35790078400 | en_HK |
dc.identifier.scopusauthorid | To, SKM=36141388100 | en_HK |
dc.identifier.citeulike | 7043064 | - |
dc.identifier.issnl | 1083-4362 | - |