Anti-holomorphic involutions of the moduli spaces of Higgs bundles
Journal de l’École polytechnique — Mathématiques, Volume 2 (2015), pp. 35-54.

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.

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.

Received:
Accepted:
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.
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
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Volume 2 (2015), pp. 35-54. doi : 10.5802/jep.16. https://jep.centre-mersenne.org/articles/10.5802/jep.16/

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