Nous montrons que les cellules de Calogero-Moser coïncident avec les cellules de Kazhdan-Lusztig pour les groupes diédraux dans le cas des paramètres égaux.
We prove that Calogero–Moser cells coincide with Kazhdan–Lusztig cells for dihedral groups in the equal parameter case.
Keywords: Calogero–Moser cells, dihedral groups
Mot clés : Cellules de Calogero–Moser, groupes diédraux
@article{AMBP_2022__29_2_187_0, author = {Bonnaf\'e, C\'edric and Germoni, J\'er\^ome}, title = {Calogero{\textendash}Moser cells of dihedral groups at equal parameters}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {187--208}, publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal}, volume = {29}, number = {2}, year = {2022}, doi = {10.5802/ambp.410}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.410/} }
TY - JOUR AU - Bonnafé, Cédric AU - Germoni, Jérôme TI - Calogero–Moser cells of dihedral groups at equal parameters JO - Annales mathématiques Blaise Pascal PY - 2022 SP - 187 EP - 208 VL - 29 IS - 2 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.410/ DO - 10.5802/ambp.410 LA - en ID - AMBP_2022__29_2_187_0 ER -
%0 Journal Article %A Bonnafé, Cédric %A Germoni, Jérôme %T Calogero–Moser cells of dihedral groups at equal parameters %J Annales mathématiques Blaise Pascal %D 2022 %P 187-208 %V 29 %N 2 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.410/ %R 10.5802/ambp.410 %G en %F AMBP_2022__29_2_187_0
Bonnafé, Cédric; Germoni, Jérôme. Calogero–Moser cells of dihedral groups at equal parameters. Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 2, pp. 187-208. doi : 10.5802/ambp.410. http://www.numdam.org/articles/10.5802/ambp.410/
[1] Generalized Calogero–Moser spaces and rational Cherednik algebras, Ph. D. Thesis, University of Edinburgh (2010)
[2] Kazhdan–Lusztig cells with unequal parameters, Algebra and Applications, 24, Springer, 2017, xxv+348 pages | DOI | MR
[3] On the Calogero-Moser space associated with dihedral groups, Ann. Math. Blaise Pascal, Volume 25 (2018) no. 2, pp. 265-298 | MR
[4] Calogero–Moser versus Kazhdan–Lusztig cells, Pac. J. Math., Volume 261 (2013) no. 1, pp. 45-51 | DOI | MR
[5] Cherednik algebras and Calogero–Moser cells (2017) | arXiv
[6] Gaudin Algebras, RSK and Calogero–Moser cells in type A (2020) (to appear in Proc. Lond. Math. Soc.) | arXiv
[7] Representations of Coxeter groups and Hecke algebras, Invent. Math., Volume 53 (1979) no. 2, pp. 165-184 | DOI | MR | Zbl
[8] Left cells in Weyl groups, Lie group representations, I (College Park, Md., 1982/1983) (Lecture Notes in Mathematics), Volume 1024, Springer, 1983, pp. 99-111 | MR | Zbl
[9] Bethe algebra of Gaudin model, Calogero–Moser space, and Cherednik algebra, Int. Math. Res. Not., Volume 2014 (2014) no. 5, pp. 1174-1204 | DOI | MR
[10] Spaces of quasi-exponentials and representations of the Yangian , Transform. Groups, Volume 19 (2014) no. 3, pp. 861-885 | DOI | MR | Zbl
Cité par Sources :