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arXiv · 2207.03147

A higher-dimensional Chevalley restriction theorem for orthogonal groups

Lei Song·Xiaopeng Xia·Jinxing Xu
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Abstract

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

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BibTeXRIS

Lei Song, Xiaopeng Xia, Jinxing Xu. 2022-07-07. A higher-dimensional Chevalley restriction theorem for orthogonal groups. https://doi.org/10.1016/j.aim.2023.109104

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