From conjugacy classes in the Weyl group to unipotent classes, II
Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map Phi[subscript p] from the set [underline W] of conjugacy classes in the Weyl group W to the set of unipotent classes in G. Here we prove three results for Phi...
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| Format: | Article |
| Language: | en_US |
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American Mathematical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/71200 https://orcid.org/0000-0001-9414-6892 |
| _version_ | 1811083769304580096 |
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| author | Lusztig, George |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George |
| author_sort | Lusztig, George |
| collection | MIT |
| description | Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map Phi[subscript p] from the set [underline W] of conjugacy classes in the Weyl group W to the set of unipotent classes in G. Here we prove three results for Phi[subscript p]. First we show that Phi[subscript p] has a canonical one-sided inverse. Next we show that Phi[subscript 0]=r Phi[subscript p for a unique map r. Finally, we construct a natural surjective map from [underline W] to the set of special representations of W which is the composition of Phi[subscript 0] with another natural map and we show that this map depends only on the Coxeter group structure of W. |
| first_indexed | 2024-09-23T12:38:46Z |
| format | Article |
| id | mit-1721.1/71200 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:38:46Z |
| publishDate | 2012 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/712002022-10-05T04:32:43Z From conjugacy classes in the Weyl group to unipotent classes, II Lusztig, George Massachusetts Institute of Technology. Department of Mathematics Lusztig, George Lusztig, George Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map Phi[subscript p] from the set [underline W] of conjugacy classes in the Weyl group W to the set of unipotent classes in G. Here we prove three results for Phi[subscript p]. First we show that Phi[subscript p] has a canonical one-sided inverse. Next we show that Phi[subscript 0]=r Phi[subscript p for a unique map r. Finally, we construct a natural surjective map from [underline W] to the set of special representations of W which is the composition of Phi[subscript 0] with another natural map and we show that this map depends only on the Coxeter group structure of W. National Science Foundation (U.S.) 2012-06-21T19:58:16Z 2012-06-21T19:58:16Z 2012-04 2011-07 Article http://purl.org/eprint/type/JournalArticle 1088-4165 http://hdl.handle.net/1721.1/71200 Lusztig, G. “From Conjugacy Classes in the Weyl Group to Unipotent Classes, II.” Representation Theory of the American Mathematical Society 16.6 (2012): 189–211. Web.© 2012 American Mathematical Society. https://orcid.org/0000-0001-9414-6892 en_US http://dx.doi.org/10.1090/S1088-4165-2012-00411-3 Representation Theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society American Mathematical Society |
| spellingShingle | Lusztig, George From conjugacy classes in the Weyl group to unipotent classes, II |
| title | From conjugacy classes in the Weyl group to unipotent classes, II |
| title_full | From conjugacy classes in the Weyl group to unipotent classes, II |
| title_fullStr | From conjugacy classes in the Weyl group to unipotent classes, II |
| title_full_unstemmed | From conjugacy classes in the Weyl group to unipotent classes, II |
| title_short | From conjugacy classes in the Weyl group to unipotent classes, II |
| title_sort | from conjugacy classes in the weyl group to unipotent classes ii |
| url | http://hdl.handle.net/1721.1/71200 https://orcid.org/0000-0001-9414-6892 |
| work_keys_str_mv | AT lusztiggeorge fromconjugacyclassesintheweylgrouptounipotentclassesii |