On isomorphisms of certain functors for Cherednik algebras
HTML articles powered by AMS MathViewer
- by Ivan Losev
- Represent. Theory 17 (2013), 247-262
- DOI: https://doi.org/10.1090/S1088-4165-2013-00437-5
- Published electronically: May 14, 2013
- PDF | Request permission
Abstract:
Bezrukavnikov and Etingof introduced some functors between the categories $\mathcal {O}$ for rational Cherednik algebras. Namely, they defined two induction functors $\mathrm {Ind}_b, \mathrm {ind}_\lambda$ and two restriction functors $\mathrm {Res}_b,\mathrm {res}_\lambda$. They conjectured that one has functor isomorphisms $\mathrm {Ind}_b\cong \mathrm {ind}_\lambda , \mathrm {Res}_b\cong \mathrm {res}_\lambda$. The goal of this paper is to prove this conjecture.References
- Roman Bezrukavnikov and Pavel Etingof, Parabolic induction and restriction functors for rational Cherednik algebras, Selecta Math. (N.S.) 14 (2009), no. 3-4, 397–425. MR 2511190, DOI 10.1007/s00029-009-0507-z
- Kenneth A. Brown and Iain Gordon, Poisson orders, symplectic reflection algebras and representation theory, J. Reine Angew. Math. 559 (2003), 193–216. MR 1989650, DOI 10.1515/crll.2003.048
- Pavel Etingof and Victor Ginzburg, Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002), no. 2, 243–348. MR 1881922, DOI 10.1007/s002220100171
- Victor Ginzburg, Nicolas Guay, Eric Opdam, and Raphaël Rouquier, On the category $\scr O$ for rational Cherednik algebras, Invent. Math. 154 (2003), no. 3, 617–651. MR 2018786, DOI 10.1007/s00222-003-0313-8
- Ivan Losev, Completions of symplectic reflection algebras, Selecta Math. (N.S.) 18 (2012), no. 1, 179–251. MR 2891864, DOI 10.1007/s00029-011-0071-1
- I. Losev. Highest weight $\mathfrak {sl}_2$-categorifications I. Crystals. arXiv:1201.4493. Accepted by Math. Zeitschrift.
- Peng Shan, Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras, Ann. Sci. Éc. Norm. Supér. (4) 44 (2011), no. 1, 147–182 (English, with English and French summaries). MR 2760196, DOI 10.24033/asens.2141
Bibliographic Information
- Ivan Losev
- Affiliation: Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115
- Email: i.loseu@neu.edu
- Received by editor(s): January 25, 2012
- Received by editor(s) in revised form: November 25, 2012
- Published electronically: May 14, 2013
- Additional Notes: The author was supported by the NSF grant DMS-0900907
- © Copyright 2013 American Mathematical Society
- Journal: Represent. Theory 17 (2013), 247-262
- MSC (2010): Primary 16G99
- DOI: https://doi.org/10.1090/S1088-4165-2013-00437-5
- MathSciNet review: 3054265