Character D-modules via Drinfeld center of Harish-Chandra bimodules
The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining functor (Radon transform) by a result of Beilinson and Ginzburg...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2012
|
| Online Access: | http://hdl.handle.net/1721.1/70519 https://orcid.org/0000-0001-5902-8989 |
| _version_ | 1811074979617308672 |
|---|---|
| author | Bezrukavnikov, Roman Finkelberg, Michael Ostrik, Viktor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Finkelberg, Michael Ostrik, Viktor |
| author_sort | Bezrukavnikov, Roman |
| collection | MIT |
| description | The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining functor (Radon transform) by a result of Beilinson and Ginzburg (Represent. Theory 3, 1–31, 1999). Exactness property of the long intertwining functor on a cell subquotient of the Harish-Chandra bimodules category shows that the truncated convolution category of Lusztig (Adv. Math. 129, 85–98, 1997) can be realized as a subquotient of the category of Harish-Chandra bimodules. Together with the description of the truncated convolution category (Bezrukavnikov et al. in Isr. J. Math. 170, 207–234, 2009) this allows us to derive (under a mild technical assumption) a classification of irreducible character sheaves over ℂ obtained by Lusztig by a different method.
We also give a simple description for the top cohomology of convolution of character sheaves over ℂ in a given cell modulo smaller cells and relate the so-called Harish-Chandra functor to Verdier specialization in the De Concini–Procesi compactification. |
| first_indexed | 2024-09-23T09:58:28Z |
| format | Article |
| id | mit-1721.1/70519 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:58:28Z |
| publishDate | 2012 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/705192022-09-26T14:55:03Z Character D-modules via Drinfeld center of Harish-Chandra bimodules Bezrukavnikov, Roman Finkelberg, Michael Ostrik, Viktor Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Bezrukavnikov, Roman The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining functor (Radon transform) by a result of Beilinson and Ginzburg (Represent. Theory 3, 1–31, 1999). Exactness property of the long intertwining functor on a cell subquotient of the Harish-Chandra bimodules category shows that the truncated convolution category of Lusztig (Adv. Math. 129, 85–98, 1997) can be realized as a subquotient of the category of Harish-Chandra bimodules. Together with the description of the truncated convolution category (Bezrukavnikov et al. in Isr. J. Math. 170, 207–234, 2009) this allows us to derive (under a mild technical assumption) a classification of irreducible character sheaves over ℂ obtained by Lusztig by a different method. We also give a simple description for the top cohomology of convolution of character sheaves over ℂ in a given cell modulo smaller cells and relate the so-called Harish-Chandra functor to Verdier specialization in the De Concini–Procesi compactification. United States. Defense Advanced Research Projects Agency (grant HR0011-04-1-0031) National Science Foundation (U.S.) (grant DMS-0625234) National Science Foundation (U.S.) (grant DMS-0854764) AG Laboratory HSE (RF government grant, ag. 11.G34.31.0023) Russian Foundation for Basic Research (grant 09-01-00242) Ministry of Education and Science of the Russian Federation (grant No. 2010-1.3.1-111-017-029) Science Foundation of the NRU-HSE (award 11-09-0033) National Science Foundation (U.S.) (grant DMS-0602263) 2012-05-04T22:02:43Z 2012-05-04T22:02:43Z 2011-09 2010-06 Article http://purl.org/eprint/type/JournalArticle 0020-9910 1432-1297 http://hdl.handle.net/1721.1/70519 Bezrukavnikov, Roman, Michael Finkelberg, and Victor Ostrik. “Character D-modules via Drinfeld Center of Harish-Chandra Bimodules.” Inventiones mathematicae (2011): n. pag. Web. 4 May 2012. © 2011 Springer-Verlag https://orcid.org/0000-0001-5902-8989 en_US http://dx.doi.org/10.1007/s00222-011-0354-3 Inventiones Mathematicae Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Bezrukavnikov, Roman Finkelberg, Michael Ostrik, Viktor Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title | Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title_full | Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title_fullStr | Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title_full_unstemmed | Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title_short | Character D-modules via Drinfeld center of Harish-Chandra bimodules |
| title_sort | character d modules via drinfeld center of harish chandra bimodules |
| url | http://hdl.handle.net/1721.1/70519 https://orcid.org/0000-0001-5902-8989 |
| work_keys_str_mv | AT bezrukavnikovroman characterdmodulesviadrinfeldcenterofharishchandrabimodules AT finkelbergmichael characterdmodulesviadrinfeldcenterofharishchandrabimodules AT ostrikviktor characterdmodulesviadrinfeldcenterofharishchandrabimodules |