Adapted pairs and Weierstrass sections

2015/03/09 by Florence Fauquant-Millet, Fauquant-Millet, Florence, Anthony Joseph +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1503.02523

openalex publication_date 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Adapted pairs and Weierstrass sections are central to the invariant theory associated to the action of an algebraic Lie algebra a on a finite dimensional vector space X. In this a need not be a semisimple Lie algebra. Here their general properties are described particularly when a is the canonical truncation of a biparabolic subalgebra of a simple Lie algebra and X is the dual of a.

Cited by

• Polynomiality for the Poisson centre of truncated maximal parabolic subalgebras
• Parabolic Adjoint Action, Weierstrass Sections and Components of the Nilfibre in Type A

Related

• Adapted pairs in type A and regular nilpotent elements
• Weierstrass sections for some truncated parabolic subalgebras
• Weierstrass sections for parabolic adjoint action in type A
• The integrality of an adapted pair
• Parabolic Adjoint Action, Weierstrass Sections and Components of the Nilfibre in Type A