no. 2
Fixed points in smooth Calogero–Moser spaces
[Points fixes dans les espaces de Calogero–Moser lisses]
Bonnafé, Cédric1 ; Maksimau, Ruslan1
1 Institut Montpelliérain Alexander Grothendieck (CNRS: UMR 5149), Université Montpellier 2, Case Courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex (France)
Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 643-678.

Nous montrons que toute composante irréductible de la variété des points fixes sous l’action de μ d dans un espace de Calogero–Moser lisse est isomorphe à un espace de Calogero–Moser associé à un autre groupe de réflexions.

We prove that every irreducible component of the fixed point variety under the action of μ d in a smooth Calogero–Moser space is isomorphic to a Calogero–Moser space associated with another reflection group.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3404
Classification : 20F55, 16G20
Keywords: reflection groups, Calogero–Moser spaces, fixed points, quiver varieties
Mot clés : groupes de réflexions, espaces de Calogero–Moser, points fixes, variétés de carquois
Bonnafé, Cédric 1 ; Maksimau, Ruslan 1

1 Institut Montpelliérain Alexander Grothendieck (CNRS: UMR 5149), Université Montpellier 2, Case Courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex (France) 
@article{AIF_2021__71_2_643_0,
     author = {Bonnaf\'e, C\'edric and Maksimau, Ruslan},
     title = {Fixed points in smooth {Calogero{\textendash}Moser} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {643--678},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {71},
     number = {2},
     year = {2021},
     doi = {10.5802/aif.3404},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.3404/}
}
TY  - JOUR
AU  - Bonnafé, Cédric
AU  - Maksimau, Ruslan
TI  - Fixed points in smooth Calogero–Moser spaces
JO  - Annales de l'Institut Fourier
PY  - 2021
SP  - 643
EP  - 678
VL  - 71
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.3404/
DO  - 10.5802/aif.3404
LA  - en
ID  - AIF_2021__71_2_643_0
ER  - 
%0 Journal Article
%A Bonnafé, Cédric
%A Maksimau, Ruslan
%T Fixed points in smooth Calogero–Moser spaces
%J Annales de l'Institut Fourier
%D 2021
%P 643-678
%V 71
%N 2
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.3404/
%R 10.5802/aif.3404
%G en
%F AIF_2021__71_2_643_0
Bonnafé, Cédric; Maksimau, Ruslan. Fixed points in smooth Calogero–Moser spaces. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 643-678. doi : 10.5802/aif.3404. http://www.numdam.org/articles/10.5802/aif.3404/

[1] Bellamy, Gwyn On singular Calogero–Moser spaces, Bull. Lond. Math. Soc., Volume 41 (2009) no. 2, pp. 315-326 | DOI | MR | Zbl

[2] Bellamy, Gwyn; Schedler, Travis; Thiel, Ulrich Hyperplane arrangements associated to symplectic quotient singularities, Phenomenological approach to algebraic geometry (Banach Center Publ.), Volume 116, Polish Academy of Sciences, Institute of Mathematics, 2018, pp. 25-45 | MR | Zbl

[3] Berg, Chris; Jones, Brant; Vazirani, Monica A bijection on core partitions and a parabolic quotient of the affine symmetric group, J. Comb. Theory, Volume 116 (2009) no. 8, pp. 1344-1360 | DOI | MR | Zbl

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

[5] Bonnafé, Cédric; Shan, Peng On the cohomology of Calogero–Moser spaces, Int. Math. Res. Not., Volume 2020 (2018) no. 4, pp. 1091-1111 | Zbl

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

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

[8] Broué, Michel; Malle, Gunter Zyklotomische Heckealgebren, Représentations unipotentes génériques et blocs des groupes réductifs finis avec un appendice de George Lusztig (Broué, Michel al, ed.) (Astérisque), Volume 212, Société Mathématique de France, 1993, pp. 119-189 | Numdam | Zbl

[9] Broué, Michel; Michel, Jean Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne–Lusztig associées, Finite reductive groups: related structures and representations. Proceedings of an international conference, Luminy, France, October 1994 (Progress in Mathematics), Volume 141, Birkhäuser, 1996, pp. 73-139 | Zbl

[10] Crawley-Boevey, William Geometry of the moment map for representations of quivers, Compos. Math., Volume 126 (2001) no. 3, pp. 257-293 | DOI | MR | Zbl

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

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

[13] Gordon, Iain Quiver varieties, category 𝒪 for rational Cherednik algebras, and Hecke algebras, IMRP, Int. Math. Res. Pap., Volume 2008 (2008), rpn006, 69 pages

[14] Kac, Victor G. Infinite Dimensional Lie Algebras – An Introduction, Progress in Mathematics, 44, Birkhäuser, 1983 | Zbl

[15] Le Bruyn, Lieven Non commutative smoothness and coadjoint orbits, J. Algebra, Volume 258 (2002) no. 1, pp. 60-70 | DOI | Zbl

[16] van Leeuwen, Marc A. A. Edge sequences, ribbon tableaux, and an action of affine permutations, Eur. J. Comb., Volume 20 (1999) no. 2, pp. 179-195 | DOI | MR | Zbl

[17] Lusztig, George Quiver varieties and Weyl group actions, Ann. Inst. Fourier, Volume 50 (2000) no. 2, pp. 461-489 | DOI | Numdam | MR | Zbl

[18] Przeździecki, Tomasz The combinatorics of ℂ * -fixed points in generalized Calogero-Moser spaces and Hilbert schemes, J. Algebra, Volume 556 (2020), pp. 936-992 | DOI | MR | Zbl

[19] Thiel, Ulrich Champ: a Cherednik algebra Magma package, LMS J. Comput. Math., Volume 18 (2015), pp. 266-307 | DOI | MR

Cité par Sources :