Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/67788 |
| _version_ | 1826197980434137088 |
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| author | Dodd, Christopher Stephen |
| author2 | Roman Bezrukavnikov. |
| author_facet | Roman Bezrukavnikov. Dodd, Christopher Stephen |
| author_sort | Dodd, Christopher Stephen |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. |
| first_indexed | 2024-09-23T10:56:47Z |
| format | Thesis |
| id | mit-1721.1/67788 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:56:47Z |
| publishDate | 2011 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/677882019-04-11T06:24:58Z Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras Dodd, Christopher Stephen Roman Bezrukavnikov. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 97-100). In this thesis, we examine three different versions of "categorification" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is by certain categories of constructible sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche. by Christopher Stephen Dodd. Ph.D. 2011-12-19T18:51:32Z 2011-12-19T18:51:32Z 2011 2011 Thesis http://hdl.handle.net/1721.1/67788 767740351 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 100 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Dodd, Christopher Stephen Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title | Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title_full | Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title_fullStr | Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title_full_unstemmed | Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title_short | Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras |
| title_sort | equivariant coherent sheaves soergel bimodules and categorification of affine hecke algebras |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/67788 |
| work_keys_str_mv | AT doddchristopherstephen equivariantcoherentsheavessoergelbimodulesandcategorificationofaffineheckealgebras |