Anti-holomorphic involutions of the moduli spaces of Higgs bundles

Indranil Biswas; Oscar García-Prada

doi:10.5802/jep.16

Anti-holomorphic involutions of the moduli spaces of Higgs bundles
[Involutions anti-holomorphes des espaces de modules de fibrés de Higgs]

Indranil Biswas ¹ ; Oscar García-Prada ²

¹ School of Mathematics, Tata Institute of Fundamental Research Homi Bhabha Road, Bombay 400005, India
² Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM Nicolás Cabrera, 13–15, 28049 Madrid, Spain

Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 35-54.

Résumé
Abstract

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 : 2014-10-22
Accepté le : 2015-01-30

MR Zbl

DOI : 10.5802/jep.16

Classification : 14H60, 57R57, 58D29
Keywords: Higgs $G$-bundle, reality condition, branes, character variety.
Mot clés : $G$-fibré de Higgs, condition de réalité, « branes », variétés caractères.

Affiliations des auteurs :

Indranil Biswas ¹ ; Oscar García-Prada ²

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Anti-holomorphic involutions of the~moduli~spaces of {Higgs} bundles},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {35--54},
     publisher = {\'Ecole polytechnique},
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Indranil Biswas; Oscar García-Prada. 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/articles/10.5802/jep.16/

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