We study anti-holomorphic involutions of the moduli space of -Higgs bundles over a compact Riemann surface , where is a complex semisimple Lie group. These involutions are defined by fixing anti-holomorphic involutions on both and . We analyze the fixed point locus in the moduli space and their relation with representations of the orbifold fundamental group of 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 -fibrés de Higgs sur une surface de Riemann compacte , où est un groupe de Lie semi-simple complexe. Ces involutions sont définies en fixant des involutions anti-holomorphes à la fois sur et . Nous en analysons le lieu des points fixes dans l’espace de modules et leur relation avec les représentation du groupe fondamental orbifold de 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.
Accepted:
DOI: 10.5802/jep.16
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
@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{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {35--54}, publisher = {\'Ecole polytechnique}, volume = {2}, year = {2015}, doi = {10.5802/jep.16}, mrnumber = {3326004}, zbl = {1333.14032}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.16/} }
TY - JOUR AU - Indranil Biswas AU - Oscar García-Prada TI - Anti-holomorphic involutions of the moduli spaces of Higgs bundles JO - Journal de l’École polytechnique — Mathématiques PY - 2015 SP - 35 EP - 54 VL - 2 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.16/ DO - 10.5802/jep.16 LA - en ID - JEP_2015__2__35_0 ER -
%0 Journal Article %A Indranil Biswas %A Oscar García-Prada %T Anti-holomorphic involutions of the moduli spaces of Higgs bundles %J Journal de l’École polytechnique — Mathématiques %D 2015 %P 35-54 %V 2 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.16/ %R 10.5802/jep.16 %G en %F JEP_2015__2__35_0
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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