Anti-holomorphic involutions of the moduli spaces of Higgs bundles
[Involutions anti-holomorphes des espaces de modules de fibrés de Higgs]
Journal de l’École polytechnique — Mathématiques, Tome 2 (2015) , pp. 35-54.

Nous étudions les involutions anti-holomorphes des espaces de modules de G-fibrés de Higgs sur une surface de Riemann compacte X, où G est un groupe de Lie semi-simple complexe. Ces involutions sont définies en fixant des involutions anti-holomorphes à la fois sur X et G. Nous en analysons le lieu des points fixes dans l’espace de modules et leur relation avec les représentation du groupe fondamental orbifold de X muni de l’involution anti-holomorphe. Nous étudions aussi la relation avec les « branes ». Ceci généralise les travaux de Biswas–García-Prada–Hurtubise et Baraglia–Schaposnik.

We study anti-holomorphic involutions of the moduli space of G-Higgs bundles over a compact Riemann surface X, where G is a complex semisimple Lie group. These involutions are defined by fixing anti-holomorphic involutions on both X and G. We analyze the fixed point locus in the moduli space and their relation with representations of the orbifold fundamental group of X equipped with the anti-holomorphic involution. We also study the relation with branes. This generalizes work by Biswas–García-Prada–Hurtubise and Baraglia–Schaposnik.

Reçu le : 2014-10-23
Accepté le : 2015-01-31
DOI : https://doi.org/10.5802/jep.16
Classification : 14H60,  57R57,  58D29
Mots clés: G-fibré de Higgs, condition de réalité, « branes », variétés caractères.
@article{JEP_2015__2__35_0,
     author = {Indranil Biswas and Oscar Garc\'\i a-Prada},
     title = {Anti-holomorphic involutions of the~moduli~spaces of Higgs bundles},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {35--54},
     publisher = {\'Ecole polytechnique},
     volume = {2},
     year = {2015},
     doi = {10.5802/jep.16},
     zbl = {1333.14032},
     mrnumber = {3326004},
     language = {en},
     url = {jep.centre-mersenne.org/item/JEP_2015__2__35_0/}
}
Biswas, Indranil; García-Prada, Oscar. Anti-holomorphic involutions of the moduli spaces of Higgs bundles. Journal de l’École polytechnique — Mathématiques, Tome 2 (2015) , pp. 35-54. doi : 10.5802/jep.16. https://jep.centre-mersenne.org/item/JEP_2015__2__35_0/

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