Algebra & Number Theory

Affinity of Cherednik algebras on projective space

Gwyn Bellamy and Maurizio Martino

Full-text: Open access

Abstract

We give sufficient conditions for the affinity of Etingof’s sheaves of Cherednik algebras on projective space. To do this, we introduce the notion of pullback of modules under certain flat morphisms.

Article information

Source
Algebra Number Theory, Volume 8, Number 5 (2014), 1151-1177.

Dates
Received: 29 July 2013
Revised: 17 February 2014
Accepted: 31 March 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730227

Digital Object Identifier
doi:10.2140/ant.2014.8.1151

Mathematical Reviews number (MathSciNet)
MR3263139

Zentralblatt MATH identifier
1329.14033

Subjects
Primary: 20C08: Hecke algebras and their representations
Secondary: 16S80: Deformations of rings [See also 13D10, 14D15]

Keywords
rational Cherednik algebras localization theory

Citation

Bellamy, Gwyn; Martino, Maurizio. Affinity of Cherednik algebras on projective space. Algebra Number Theory 8 (2014), no. 5, 1151--1177. doi:10.2140/ant.2014.8.1151. https://projecteuclid.org/euclid.ant/1513730227


Export citation

References

  • A. Beilinson and J. Bernstein, antzen conjectures”}, pp. 1–50 in I. M. Gel'fand Seminar, edited by S. Gel'fand and S. Gindikin, Adv. Soviet Math. 16, Amer. Math. Soc., Providence, RI, 1993.
  • M. Van den Bergh, “Differential operators on semi-invariants for tori and weighted projective spaces”, pp. 255–272 in Topics in invariant theory (Paris, 1989–1990), edited by M.-P. Malliavin, Lecture Notes in Math. 1478, Springer, Berlin, 1991. http://msp.org/idx/zbl/0802.13005Zbl 0802.13005
  • D. Bessis, C. Bonnafé, and R. Rouquier, “Quotients et extensions de groupes de réflexion”, Math. Ann. 323:3 (2002), 405–436.
  • W. Borho and J.-L. Brylinski, “Differential operators on homogeneous spaces, II: Relative enveloping algebras”, Bull. Soc. Math. France 117:2 (1989), 167–210.
  • T. Chmutova, “Twisted symplectic reflection algebras”, preprint, 2005. http://www.arxiv.org/abs/math/0505653arXiv math/0505653
  • P. Etingof, “Cherednik and Hecke algebras of varieties with a finite group action”, preprint, 2004.
  • P. Etingof and V. Ginzburg, “Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism”, Invent. Math. 147:2 (2002), 243–348.
  • W. Fulton, Intersection theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics 2, Springer, Berlin, 1998.
  • V. Ginzburg, N. Guay, E. Opdam, and R. Rouquier, “On the category $\mathcal{{O}}$ for rational Cherednik algebras”, Invent. Math. 154:3 (2003), 617–651.
  • R. Hotta, K. Takeuchi, and T. Tanisaki, $D$-modules, perverse sheaves, and representation theory, Progress in Mathematics 236, Birkhäuser, Boston, 2008.
  • M. Kashiwara, “Representation theory and $D$-modules on flag varieties”, pp. 55–109 in Orbites unipotentes et représentations, III: Orbites et faisceaux pervers, Astérisque 173-174, Soc. Math. France, Paris, 1989.
  • H. Matsumura, Commutative ring theory, 2nd ed., Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, 1989.
  • J. S. Milne, Étale cohomology, Princeton Mathematical Series 33, Princeton University Press, 1980.
  • R. P. Stanley, “Relative invariants of finite groups generated by pseudoreflections”, J. Algebra 49:1 (1977), 134–148.
  • S. J. Wilcox, Representations of the rational Cherednik algebra, thesis, Harvard University, Cambridge, MA, 2011, http://search.proquest.com/docview/878131539.