no. 2
On the Calogero–Moser space associated with dihedral groups
Cédric Bonnafé1
1 Institut Montpelliérain Alexander Grothendieck (CNRS: UMR 5149) Université Montpellier 2 Case Courrier 051 Place Eugène Bataillon 34095 Montpellier, France
Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 2, pp. 265-298.

We investigate some geometric properties of the Calogero–Moser spaces associated with a dihedral group. As a consequence, we check in this particular case some conjectures made by the author and Raphaël Rouquier about general Calogero–Moser spaces.

Publié le :
DOI : 10.5802/ambp.377

Cédric Bonnafé 1

1 Institut Montpelliérain Alexander Grothendieck (CNRS: UMR 5149) Université Montpellier 2 Case Courrier 051 Place Eugène Bataillon 34095 Montpellier, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AMBP_2018__25_2_265_0,
     author = {C\'edric Bonnaf\'e},
     title = {On the {Calogero{\textendash}Moser} space associated with dihedral groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {265--298},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {25},
     number = {2},
     year = {2018},
     doi = {10.5802/ambp.377},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.377/}
}
TY  - JOUR
AU  - Cédric Bonnafé
TI  - On the Calogero–Moser space associated with dihedral groups
JO  - Annales mathématiques Blaise Pascal
PY  - 2018
SP  - 265
EP  - 298
VL  - 25
IS  - 2
PB  - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.377/
DO  - 10.5802/ambp.377
LA  - en
ID  - AMBP_2018__25_2_265_0
ER  - 
%0 Journal Article
%A Cédric Bonnafé
%T On the Calogero–Moser space associated with dihedral groups
%J Annales mathématiques Blaise Pascal
%D 2018
%P 265-298
%V 25
%N 2
%I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.377/
%R 10.5802/ambp.377
%G en
%F AMBP_2018__25_2_265_0
Cédric Bonnafé. On the Calogero–Moser space associated with dihedral groups. Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 2, pp. 265-298. doi : 10.5802/ambp.377. https://ambp.centre-mersenne.org/articles/10.5802/ambp.377/

[1] Jacques Alev; Loïc Foissy Le groupe des traces de Poisson de certaines algèbres d’invariants, Commun. Algebra, Volume 37 (2009) no. 1, pp. 368-388 | DOI | MR

[2] Gwyn Bellamy Generalized Calogero-Moser spaces and rational Cherednik algebras, University of Edinburgh (UK) (2010) (Ph. D. Thesis)

[3] Gwyn Bellamy Cuspidal representations of rational Cherednik algebras at t=0, Math. Z., Volume 269 (2011) no. 3-4, pp. 609-627 | DOI | MR

[4] Gwyn Bellamy; Ulrich Thiel Cuspidal Calogero-Moser and Lusztig families for Coxeter groups, J. Algebra, Volume 462 (2016), pp. 197-252 | DOI | MR

[5] Yuri Berest; Pavel Etingof; Victor Ginzburg Cherednik algebras and differential operators on quasi-invariants, Duke Math. J., Volume 118 (2003) no. 2, pp. 279-337 | DOI | MR

[6] Cédric Bonnafé; Raphaël Rouquier Cherednik algebras and Calogero-Moser cells (2017) (https://arxiv.org/abs/1708.09764)

[7] Cédric Bonnafé; Ulrich Thiel Calogero-Moser families and cellular characters: computational aspects (in preparation)

[8] Wieb Bosma; John Cannon; Catherine Playoust The Magma algebra system. I. The user language, J. Symb. Comput., Volume 24 (1997) no. 3-4, pp. 235-265 | DOI | MR | Zbl

[9] Charlotte Dezélée Représentations de dimension finie de l’algèbre de Cherednik rationnelle, Bull. Soc. Math. Fr., Volume 131 (2003) no. 4, pp. 465-482 | MR

[10] John D. Dixon; Brian Mortimer Permutation groups, Graduate Texts in Mathematics, 163, Springer, 1996, xii+346 pages | DOI | MR

[11] Pavel Etingof; Victor Ginzburg Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math., Volume 147 (2002) no. 2, pp. 243-348 | DOI | MR

[12] GAP – Groups, Algorithms, and Programming, Version 4.9.1 (2018) (https://www.gap-system.org)

[13] Iain Gordon Baby Verma modules for rational Cherednik algebras, Bull. Lond. Math. Soc., Volume 35 (2003) no. 3, pp. 321-336 | DOI | MR

[14] Iain Gordon; Maurizio Martino Calogero-Moser space, restricted rational Cherednik algebras and two-sided cells, Math. Res. Lett., Volume 16 (2009) no. 2, pp. 255-262 | DOI | MR

[15] George Lusztig Hecke algebras with unequal parameters, CRM Monograph Series, 18, American Mathematical Society, 2003, vi+136 pages | MR | Zbl

[16] Ulrich Thiel Champ: a Cherednik algebra Magma package, LMS J. Comput. Math., Volume 18 (2015) no. 1, pp. 266-307 | DOI | MR | Zbl

  • Cédric Bonnafé On the Calogero–Moser space associated with dihedral groups II. The equal parameter case, Annales mathématiques Blaise Pascal, Volume 30 (2024) no. 2, p. 115 | DOI:10.5802/ambp.419
  • Mátyás Domokos Syzygies for the vector invariants of the dihedral group, Journal of Algebra, Volume 641 (2024), p. 9 | DOI:10.1016/j.jalgebra.2023.10.037
  • Cédric Bonnafé; Jérôme Germoni Calogero–Moser cells of dihedral groups at equal parameters, Annales mathématiques Blaise Pascal, Volume 29 (2023) no. 2, p. 187 | DOI:10.5802/ambp.410
  • Adrien Brochier; Iain Gordon; Noah White Gaudin algebras, RSK and Calogero–Moser cells in Type A, Proceedings of the London Mathematical Society, Volume 126 (2023) no. 5, p. 1467 | DOI:10.1112/plms.12506
  • Gwyn Bellamy; Cédric Bonnafé; Baohua Fu; Daniel Juteau; Paul Levy; Eric Sommers A new family of isolated symplectic singularities with trivial local fundamental group, Proceedings of the London Mathematical Society, Volume 126 (2023) no. 5, p. 1496 | DOI:10.1112/plms.12513
  • Cédric Bonnafé; Ulrich Thiel Computational aspects of Calogero–Moser spaces, Selecta Mathematica, Volume 29 (2023) no. 5 | DOI:10.1007/s00029-023-00878-3
  • Nicolas Jacon; Abel Lacabanne On Calogero–Moser cellular characters for imprimitive complex reflection groups, Tunisian Journal of Mathematics, Volume 5 (2023) no. 4, p. 605 | DOI:10.2140/tunis.2023.5.605
  • Hendrik De Bie; Alexis Langlois-Rémillard; Roy Oste; Joris Van der Jeugt Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl–Dirac operator, Journal of Algebra, Volume 591 (2022), p. 170 | DOI:10.1016/j.jalgebra.2021.09.025
  • Abel Lacabanne On a conjecture about cellular characters for the complex reflection group G(d,1,n), Annales Mathématiques Blaise Pascal, Volume 27 (2020) no. 1, p. 37 | DOI:10.5802/ambp.390

Cité par 9 documents. Sources : Crossref