Etingof’s conjecture for quantized quiver varieties
We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coor...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/129811 |
| _version_ | 1811088500106199040 |
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| author | Bezrukavnikov, Roman |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman |
| author_sort | Bezrukavnikov, Roman |
| collection | MIT |
| description | We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof’s conjecture on the number of finite dimensional irreducible representations for Symplectic reflection algebras associated to wreath-product groups. We use several different techniques, the two principal ones are categorical Kac–Moody actions and wall-crossing functors. |
| first_indexed | 2024-09-23T14:03:08Z |
| format | Article |
| id | mit-1721.1/129811 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:03:08Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1298112022-10-01T18:52:01Z Etingof’s conjecture for quantized quiver varieties Bezrukavnikov, Roman Massachusetts Institute of Technology. Department of Mathematics We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof’s conjecture on the number of finite dimensional irreducible representations for Symplectic reflection algebras associated to wreath-product groups. We use several different techniques, the two principal ones are categorical Kac–Moody actions and wall-crossing functors. National Science Foundation (U.S.) (Grant DMS-1102434) 2021-02-18T15:22:43Z 2021-02-18T15:22:43Z 2020-10-23 2017-04 2021-02-10T04:31:03Z Article http://purl.org/eprint/type/JournalArticle 0020-9910 https://hdl.handle.net/1721.1/129811 Bezrukavnikov, Roman; Losev, Ivan. “Etingof’s conjecture for quantized quiver varieties.” Inventiones mathematicae, 223 (October 2020): 1097–1226 © 2020 The Author(s) en https://doi.org/10.1007/s00222-020-01007-z Inventiones mathematicae Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Bezrukavnikov, Roman Etingof’s conjecture for quantized quiver varieties |
| title | Etingof’s conjecture for quantized quiver varieties |
| title_full | Etingof’s conjecture for quantized quiver varieties |
| title_fullStr | Etingof’s conjecture for quantized quiver varieties |
| title_full_unstemmed | Etingof’s conjecture for quantized quiver varieties |
| title_short | Etingof’s conjecture for quantized quiver varieties |
| title_sort | etingof s conjecture for quantized quiver varieties |
| url | https://hdl.handle.net/1721.1/129811 |
| work_keys_str_mv | AT bezrukavnikovroman etingofsconjectureforquantizedquivervarieties |