A higher-dimensional Chevalley restriction theorem for orthogonal groups

• 主讲人：Jinxing Xu (University of Science and Technology of China)
• 举办方： Beijing-Novosibirsk Seminar on Geometry and Mathematical Physics
• 时间： 2023-04-20 17:00 - 2023-04-20 18:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/59108A9C0E7650C20621084CA1F64AD5
Valid Until: 2027-05-31 23:59

 

Abstract: 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, Chen and Ngo conjectured a multi-variable generalization of the Chevalley restriction theorem, and they proved the GL and Sp cases. We then prove the orthogonal group case and our treatment can apply to the GL and Sp cases in a uniform way. This result has some interesting corollaries on the determinants and Pfaffians for commutative skew symmetric matrices over an arbitrary char. 0 commutative ring. This is a joint work with Lei Song and Xiaopeng Xia.

 

Bio: Jinxing Xu is an associate professor at the School of Mathematical Sciences, University of Science and Technology of China. He received PhD at Peking University in 2011 (supervisor: Acad. Gang TIAN). Xu specializes in Algebraic Geometry and has obtained a number of original results on the moduli spaces of Calabi-Yau varieties and the cohomology group of p-adic algebraic varieties. He has published several papers on Adv. Math., Int. Math. Res. Not. etc.