Invariant theory for the commuting scheme of symplectic Lie algebras

2021/02/03 by Tsao-Hsien Chen, Chen, Tsao-Hsien, Ngô Bảo Châu +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2102.01849

openalex publication_date 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Chevalley restriction theorem for the commuting scheme of symplectic Lie algebras. The key step is the construction of the inverse map of the Chevalley restriction map called the spectral data map. Along the way, we establish a certain multiplicative property of the Pfaffian which is of independent interest.

Citations

• The invariant theory of n × n matrices

Cited by

• Invariant algebraic D-modules over affine algebraic groups
• On the normality of commuting scheme for general linear Lie algebra

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