Comptes Rendus
no. 1
Algèbres de Lie, Géométrie algèbrique
Diagrams for nonabelian Hodge spaces on the affine line
[Diagrammes pour les espaces de Hodge non abéliens sur la droite affine]
Philip Boalch1 ; Daisuke Yamakawa2
1 Institut de Mathématiques de Jussieu – Paris Rive Gauche, Université de Paris et CNRS, Bâtiment Sophie Germain, 8 Place Aurélie Nemours, 75205 Paris, France
2 Department of Mathematics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 59-65.

Dans cette note, un diagramme est associé à chaque espace de Hodge non abélien sur la droite affine.

In this announcement a diagram will be defined for each nonabelian Hodge space on the affine line.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.11
Philip Boalch 1 ; Daisuke Yamakawa 2

1 Institut de Mathématiques de Jussieu – Paris Rive Gauche, Université de Paris et CNRS, Bâtiment Sophie Germain, 8 Place Aurélie Nemours, 75205 Paris, France
2 Department of Mathematics, Faculty of Science Division I, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2020__358_1_59_0,
     author = {Philip Boalch and Daisuke Yamakawa},
     title = {Diagrams for nonabelian {Hodge} spaces on the affine line},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {59--65},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.11},
     language = {en},
}
TY  - JOUR
AU  - Philip Boalch
AU  - Daisuke Yamakawa
TI  - Diagrams for nonabelian Hodge spaces on the affine line
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 59
EP  - 65
VL  - 358
IS  - 1
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.11
LA  - en
ID  - CRMATH_2020__358_1_59_0
ER  - 
%0 Journal Article
%A Philip Boalch
%A Daisuke Yamakawa
%T Diagrams for nonabelian Hodge spaces on the affine line
%J Comptes Rendus. Mathématique
%D 2020
%P 59-65
%V 358
%N 1
%I Académie des sciences, Paris
%R 10.5802/crmath.11
%G en
%F CRMATH_2020__358_1_59_0
Philip Boalch; Daisuke Yamakawa. Diagrams for nonabelian Hodge spaces on the affine line. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 59-65. doi : 10.5802/crmath.11. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.11/

[1] Philip Boalch Symplectic manifolds and isomonodromic deformations, Adv. Math., Volume 163 (2001) no. 2, pp. 137-205 | DOI | MR | Zbl

[2] Philip Boalch Irregular connections and Kac–Moody root systems (2008) (https://arxiv.org/abs/0806.1050)

[3] Philip Boalch Quivers and difference Painlevé equations, Groups and symmetries. From Neolithic Scots to John McKay (CRM Proceedings & Lecture Notes), Volume 47, American Mathematical Society, 2009, pp. 25-51 | MR | Zbl

[4] Philip Boalch Simply-laced isomonodromy systems, Publ. Math., Inst. Hautes Étud. Sci., Volume 116 (2012) no. 1, pp. 1-68 | DOI | MR | Zbl

[5] Philip Boalch Global Weyl groups and a new theory of multiplicative quiver varieties, Geom. Topol., Volume 19 (2015) no. 6, pp. 3467-3536 | DOI | MR | Zbl

[6] Philip Boalch Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams, Geometry and Physics II. A festschrift in honour of Nigel Hitchin, Oxford University Press, 2018, pp. 425-446 | MR | Zbl

[7] Philip Boalch Topology of the Stokes phenomenon (2019) (https://arxiv.org/abs/1903.12612)

[8] Philip Boalch; Daisuke Yamakawa Twisted wild character varieties (2015) (https://arxiv.org/abs/1512.08091)

[9] Andrew S. Dancer Dihedral singularities and gravitational instantons, J. Geom. Phys., Volume 12 (1993) no. 2, pp. 77-91 | DOI | MR | Zbl

[10] Rene Garnier Sur des équations différentielles du troisième ordre dont l’intégrale générale est uniforme et sur une classe d’équations nouvelles d’ordre supérieur dont l’intégrale générale a ses points critiques fixes, Ann. Sci. Éc. Norm. Supér., Volume 29 (1912), pp. 1-126 | DOI | Zbl

[11] Kazuki Hiroe Linear differential equations on the Riemann sphere and representations of quivers, Duke Math. J., Volume 166 (2017) no. 5, pp. 855-935 | DOI | MR | Zbl

[12] Kazuki Hiroe; Daisuke Yamakawa Moduli spaces of meromorphic connections and quiver varieties, Adv. Math., Volume 266 (2014), pp. 120-151 | DOI | MR | Zbl

[13] Michio Jimbo; Tetsuji Miwa Monodromy preserving deformations of linear differential equations with rational coefficients II, Physica D: Nonlinear Phenomena, Volume 2 (1981) no. 3, pp. 407-448 | DOI | MR | Zbl

[14] Nalini Joshi; Alexander V. Kitaev; P. A. Treharne On the linearization of the Painlevé III-VI equations and reductions of the three-wave resonant system, J. Math. Phys., Volume 48 (2007) no. 10, 103512, 42 pages | Zbl

[15] Bernard Malgrange Équations différentielles à coefficients polynomiaux, Progress in Mathematics, 96, Birkhäuser, 1991 | Zbl

[16] Kazuo Okamoto The Painlevé equations and the Dynkin diagrams, Painlevé transcendents: their asymptotics and physical applications (Sainte-Adèle, 1990) (NATO ASI Series. Series B. Physics), Volume 278, Plenum Press, 1990, pp. 299-313 | DOI | MR | Zbl

[17] Hidetaka Sakai Rational surfaces associated with affine root systems and geometry of the Painlevé equations, Commun. Math. Phys., Volume 220 (2001) no. 1, pp. 165-229 | DOI | MR | Zbl

[18] Daisuke Yamakawa Quiver varieties with multiplicities, Weyl groups of non-symmetric Kac-Moody algebras, and Painlevé equations, SIGMA, Symmetry Integrability Geom. Methods Appl., Volume 6 (2010), 087, 43 pages | MR | Zbl

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

On the moduli spaces of framed logarithmic connections on a Riemann surface

Indranil Biswas; Michi-aki Inaba; Arata Komyo; ...

C. R. Math (2021)

The master Painlevé VI heat equation

Robert Conte; Ivan Dornic

C. R. Math (2014)