On the Calogero–Moser space associated with dihedral groups
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 : 2018-11-28
DOI : https://doi.org/10.5802/ambp.377
@article{AMBP_2018__25_2_265_0,
     author = {C\'edric Bonnaf\'e},
     title = {On the Calogero--Moser space associated with dihedral groups},
     journal = {Annales Math\'ematiques Blaise Pascal},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {25},
     number = {2},
     year = {2018},
     pages = {265-298},
     doi = {10.5802/ambp.377},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2018__25_2_265_0/}
}
Bonnafé, Cédric. 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/item/AMBP_2018__25_2_265_0/

[1] Jacques Alev; Loïc Foissy Le groupe des traces de Poisson de certaines algèbres d’invariants, Commun. Algebra, Tome 37 (2009) no. 1, pp. 368-388 | Article | MR 2482828

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

[3] Gwyn Bellamy Cuspidal representations of rational Cherednik algebras at t=0, Math. Z., Tome 269 (2011) no. 3-4, pp. 609-627 | Article | MR 2860254

[4] Gwyn Bellamy; Ulrich Thiel Cuspidal Calogero-Moser and Lusztig families for Coxeter groups, J. Algebra, Tome 462 (2016), pp. 197-252 | Article | MR 3519506

[5] Yuri Berest; Pavel Etingof; Victor Ginzburg Cherednik algebras and differential operators on quasi-invariants, Duke Math. J., Tome 118 (2003) no. 2, pp. 279-337 | Article | MR 1980996

[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., Tome 24 (1997) no. 3-4, pp. 235-265 | Article | MR 1484478 | Zbl 0898.68039

[9] Charlotte Dezélée Représentations de dimension finie de l’algèbre de Cherednik rationnelle, Bull. Soc. Math. Fr., Tome 131 (2003) no. 4, pp. 465-482 | MR 2044491

[10] John D. Dixon; Brian Mortimer Permutation groups, Graduate Texts in Mathematics, Tome 163, Springer, 1996, xii+346 pages | Article | MR 1409812

[11] Pavel Etingof; Victor Ginzburg Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math., Tome 147 (2002) no. 2, pp. 243-348 | Article | MR 1881922

[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., Tome 35 (2003) no. 3, pp. 321-336 | Article | MR 1960942

[14] Iain Gordon; Maurizio Martino Calogero-Moser space, restricted rational Cherednik algebras and two-sided cells, Math. Res. Lett., Tome 16 (2009) no. 2, pp. 255-262 | Article | MR 2496742

[15] George Lusztig Hecke algebras with unequal parameters, CRM Monograph Series, Tome 18, American Mathematical Society, 2003, vi+136 pages | MR 1974442 | Zbl 1051.20003

[16] Ulrich Thiel Champ: a Cherednik algebra Magma package, LMS J. Comput. Math., Tome 18 (2015) no. 1, pp. 266-307 | Article | MR 3361642 | Zbl 1319.16036