Geodesic
Infinite transitivity on the Calogero–Moser space $\mathcal{C}_2$
Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 227-250 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove a particular case of the conjecture of Berest–Eshmatov–Eshmatov by showing that the group of unimodular automorphisms of $\mathbb{C}[ x,y]$ acts in an infinitely-transitive way on the Calogero-Moser space $\mathcal{C}_2$.
Keywords: infinite transitivity.
Mots-clés : Calogero–Moser space 
@article{ADM_2021_31_2_a4,
     author = {J. Kesten and S. Mathers and Z. Normatov},
     title = {Infinite transitivity on the {Calogero{\textendash}Moser} space~$\mathcal{C}_2$},
     journal = {Algebra and discrete mathematics},
     pages = {227--250},
     year = {2021},
     volume = {31},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a4/}
}
TY  - JOUR
AU  - J. Kesten
AU  - S. Mathers
AU  - Z. Normatov
TI  - Infinite transitivity on the Calogero–Moser space $\mathcal{C}_2$
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 227
EP  - 250
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a4/
LA  - en
ID  - ADM_2021_31_2_a4
ER  - 
%0 Journal Article
%A J. Kesten
%A S. Mathers
%A Z. Normatov
%T Infinite transitivity on the Calogero–Moser space $\mathcal{C}_2$
%J Algebra and discrete mathematics
%D 2021
%P 227-250
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a4/
%G en
%F ADM_2021_31_2_a4
J. Kesten; S. Mathers; Z. Normatov. Infinite transitivity on the Calogero–Moser space $\mathcal{C}_2$. Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 227-250. http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a4/

[1] Yu. Berest, A. Eshmatov, F. Eshmatov, “Multitransivity of Calogero-Moser spaces”, Transform. Groups, 21 (2016), 35–50 | DOI | MR | Zbl

[2] V. Drensky, E. Formanek, Polynomial Identity Rings, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel, 2004 | MR | Zbl

[3] K. Kuyumzhiyan, “Infinite transitivity for Calogero-Moser spaces”, Proc. Amer. Math. Soc., 148 (2020), 3723–3731 ; arXiv: 1807.05723 | DOI | MR | Zbl

[4] G. Wilson, “Collisions of Calogero-Moser particles and an adelic Grassmannian”, with an appendix by I. G. Macdonald, Invent. Math., 133 (1998), 1–41 | DOI | MR | Zbl

[5] W. Van der Kulk, “On polynomial rings in two variables”, Nieuw Arch. Wisk., 1 (1953), 33–41 | MR | Zbl