Mirabolic Robinson-Shensted-Knuth correspondence
The set of orbits of GL(V) in Fl(V) × Fl(V) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Magyar, Weyman, and Zelevinsky. We describe a mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of...
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| Format: | Article |
| Language: | en_US |
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Birkhäuser Basel
2009
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| Online Access: | http://hdl.handle.net/1721.1/49482 https://orcid.org/0000-0001-6894-2385 |
| _version_ | 1811087233096089600 |
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| author | Travkin, Roman |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Travkin, Roman |
| author_sort | Travkin, Roman |
| collection | MIT |
| description | The set of orbits of GL(V) in Fl(V) × Fl(V) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Magyar, Weyman, and Zelevinsky. We describe a mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan–Lusztig cells in the bimodule over the Iwahori–Hecke algebra of GL(V) arising from Fl(V) × Fl(V) × V. We also give conjectural applications to the classification of unipotent mirabolic character sheaves on GL(V) × V. |
| first_indexed | 2024-09-23T13:42:10Z |
| format | Article |
| id | mit-1721.1/49482 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:42:10Z |
| publishDate | 2009 |
| publisher | Birkhäuser Basel |
| record_format | dspace |
| spelling | mit-1721.1/494822022-10-01T16:36:19Z Mirabolic Robinson-Shensted-Knuth correspondence Travkin, Roman Massachusetts Institute of Technology. Department of Mathematics Travkin, Roman Travkin, Roman The set of orbits of GL(V) in Fl(V) × Fl(V) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Magyar, Weyman, and Zelevinsky. We describe a mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan–Lusztig cells in the bimodule over the Iwahori–Hecke algebra of GL(V) arising from Fl(V) × Fl(V) × V. We also give conjectural applications to the classification of unipotent mirabolic character sheaves on GL(V) × V. 2009-10-19T13:41:07Z 2009-10-19T13:41:07Z 2009-04 Article http://purl.org/eprint/type/SubmittedJournalArticle 1022-1824 1420-9020 http://hdl.handle.net/1721.1/49482 R. Travkin, “Mirabolic Robinson–Shensted–Knuth correspondence,” Selecta Mathematica, New Series, vol. 14, May. 2009, pp. 727-758. https://orcid.org/0000-0001-6894-2385 en_US http://dx.doi.org/10.1007/s00029-009-0508-y Selecta Mathematica, New Series 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. http://www.springerlink.com/help/disclaimer.mpx application/pdf Birkhäuser Basel Roman Travkin |
| spellingShingle | Travkin, Roman Mirabolic Robinson-Shensted-Knuth correspondence |
| title | Mirabolic Robinson-Shensted-Knuth correspondence |
| title_full | Mirabolic Robinson-Shensted-Knuth correspondence |
| title_fullStr | Mirabolic Robinson-Shensted-Knuth correspondence |
| title_full_unstemmed | Mirabolic Robinson-Shensted-Knuth correspondence |
| title_short | Mirabolic Robinson-Shensted-Knuth correspondence |
| title_sort | mirabolic robinson shensted knuth correspondence |
| url | http://hdl.handle.net/1721.1/49482 https://orcid.org/0000-0001-6894-2385 |
| work_keys_str_mv | AT travkinroman mirabolicrobinsonshenstedknuthcorrespondence |