ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra
© 2018 American Mathematical Society. In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a simple Lie algebra g together with a ℤ/mℤ-grading ⊕i∈ℤ/mℤ gi and a block of DG0 (gi)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Mathematical Society (AMS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135640 |
| _version_ | 1811071843310764032 |
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| author | Lusztig, George Yun, Zhiwei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George Yun, Zhiwei |
| author_sort | Lusztig, George |
| collection | MIT |
| description | © 2018 American Mathematical Society. In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a simple Lie algebra g together with a ℤ/mℤ-grading ⊕i∈ℤ/mℤ gi and a block of DG0 (gi) as introduced in [J. Represent. Theory 21 (2017), pp. 277-321], we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. This generalizes results of Vasserot [Duke Math J. 126 (2005), pp. 251-323] and Oblomkov- Yun [Adv. Math 292 (2016), pp. 601-706] which correspond to the case of the principal block. |
| first_indexed | 2024-09-23T08:56:54Z |
| format | Article |
| id | mit-1721.1/135640 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:56:54Z |
| publishDate | 2021 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/1356402023-12-14T15:43:10Z ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra Lusztig, George Yun, Zhiwei Massachusetts Institute of Technology. Department of Mathematics © 2018 American Mathematical Society. In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a simple Lie algebra g together with a ℤ/mℤ-grading ⊕i∈ℤ/mℤ gi and a block of DG0 (gi) as introduced in [J. Represent. Theory 21 (2017), pp. 277-321], we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. This generalizes results of Vasserot [Duke Math J. 126 (2005), pp. 251-323] and Oblomkov- Yun [Adv. Math 292 (2016), pp. 601-706] which correspond to the case of the principal block. 2021-10-27T20:24:24Z 2021-10-27T20:24:24Z 2018 2019-11-14T18:55:19Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135640 en 10.1090/ERT/515 Representation Theory of the American Mathematical Society 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 (AMS) American Mathematical Society |
| spellingShingle | Lusztig, George Yun, Zhiwei ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title | ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title_full | ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title_fullStr | ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title_full_unstemmed | ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title_short | ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra |
| title_sort | z ����z graded lie algebras and perverse sheaves iii graded double affine hecke algebra |
| url | https://hdl.handle.net/1721.1/135640 |
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