SL(∞, R), Higgs bundles, and quantization

Olivier Biquard (1, 2)

1 SU - Sorbonne Université
2 DMA - Département de Mathématiques et Applications - ENS Paris

Nigel Hitchin recently proposed a theory of SL(∞, R)-Higgs bundles which should parametrize a Hitchin component of representations of surface groups into SL(∞, R). We discuss some properties and propose a formal approximation of SL(∞, R) representations by SL(n, R) representations when n goes to infinity.

Domaines: Géométrie différentielle [math.DG]

Olivier Biquard. SL(∞, R), Higgs bundles, and quantization. Geometry and physics. Vol. II. A Festschrift in honour of Nigel Hitchin. Edited by Jørgen Ellegaard Andersen, Andrew Dancer and Oscar García-Prada., 2018. ⟨hal-03740918⟩