A higher-dimensional Chevalley restriction theorem for orthogonal groups

We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ngô reductive groups. In characteristic p>2, we also weaker statement. 0, the implies that categorical quotient of commuting scheme diagonal adjoint action group is integral normal. As applications, deduce some trace identities certain multiplicative property Pfaffian over an arbitrary commutative algebra.