On the L-infinity description of the Hitchin Map

TL;DR

This paper extends recent L-infinity algebraic descriptions of the Hitchin map from Higgs pairs to principal G-Higgs bundles, revealing a Lie-algebraic analogue for the adjoint quotient.

Contribution

It generalizes the L-infinity framework for the Hitchin map to principal G-Higgs bundles, connecting it with Lie algebraic structures.

Findings

L-infinity morphism induces the Hitchin map for principal G-Higgs bundles

Analogous Lie-algebraic structures are identified for the adjoint quotient

Results extend previous work on Higgs pairs to a broader class of bundles

Abstract

Recently, E.Martinengo obtained results on obstructions to deformations of Higgs pairs by describing an L-infinity morphism inducing the Hitchin map. In this note we show that analogous results hold for principal G-Higgs bundles, where G is a complex reductive group. We show that the L-infinity morphism has a Lie-algebraic analogue inducing the adjoint quotient morphism.