GdT Géométrie Algébrique Complexe

Commuting scheme, Chevalley restriction theorem and Hitchin morphism

by Jinxing Xu (University of Science and Technology of China)

Salle Picard (IMT)

Salle Picard



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.