The classical Chevalley restriction theorem asserts that for a semisimple complex Lie group G, the ring of G-invariant polynomials on the Lie algebra g is isomorphic through restriction to the ring of Weyl group invariant polynomials on the Cartan subalgebra. In studying the Hitchin morphism of principal G-Higgs bundles over higher dimensional varieties, Tsao-Hsien Chen and Ngo Bao Chau proposed a conjectured multi-variable version of the Chevalley restriction theorem, and they related it to the image of the Hitchin morphism. I will explain their program and show a proof of this generalised Chevalley restriction theorem for classical groups. Based on joint work with Lei Song and Xiaopeng Xia.
