Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 
 

 

On isomorphisms of certain functors for Cherednik algebras


Author: Ivan Losev
Journal: Represent. Theory 17 (2013), 247-262
MSC (2010): Primary 16G99
DOI: https://doi.org/10.1090/S1088-4165-2013-00437-5
Published electronically: May 14, 2013
MathSciNet review: 3054265
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BE] 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 (2010e:20007), https://doi.org/10.1007/s00029-009-0507-z
  • [BG] Kenneth A. Brown and Iain Gordon, Poisson orders, symplectic reflection algebras and representation theory, J. Reine Angew. Math. 559 (2003), 193-216. MR 1989650 (2004i:16025), https://doi.org/10.1515/crll.2003.048
  • [EG] 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 (2003b:16021), https://doi.org/10.1007/s002220100171
  • [GGOR] Victor Ginzburg, Nicolas Guay, Eric Opdam, and Raphaël Rouquier, On the category $ \mathcal {O}$ for rational Cherednik algebras, Invent. Math. 154 (2003), no. 3, 617-651. MR 2018786 (2005f:20010), https://doi.org/10.1007/s00222-003-0313-8
  • [L1] Ivan Losev, Completions of symplectic reflection algebras, Selecta Math. (N.S.) 18 (2012), no. 1, 179-251. MR 2891864, https://doi.org/10.1007/s00029-011-0071-1
  • [L2] I. Losev. Highest weight $ \mathfrak{sl}_2$-categorifications I. Crystals. arXiv:1201.4493. Accepted by Math. Zeitschrift.
  • [S] 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 (2012c:20009)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 16G99

Retrieve articles in all journals with MSC (2010): 16G99


Additional Information

Ivan Losev
Affiliation: Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115
Email: i.loseu@neu.edu

DOI: https://doi.org/10.1090/S1088-4165-2013-00437-5
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
Article copyright: © Copyright 2013 American Mathematical Society

American Mathematical Society