发表机构
Université Jean Monnet; Centrale Lyon; INSA Lyon; Université Lyon 1; CNRS, ICJ UMR5208（让·莫奈大学; 里昂中央理工学院; 里昂国立应用科学学院; 里昂第一大学; 法国国家科学研究中心，ICJ联合研究实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究A型中特定伊诺尼-维格纳收缩相关的不变量代数的多项式性，证明当抛物子代数的莱维因子分解为三个对称块且中心块与两端块大小不同时，相关代数为多项式代数。
AI 中文摘要
本文研究与A型中某些特定伊诺尼-维格纳（Inönü-Wigner）收缩相关的对称不变量代数（或由对称半不变量生成的代数）的多项式性。更准确地说，我们关注A型中某些抛物子代数相对于其分解为莱维因子（Levi factor）和幂零根基的收缩，其中幂零根基成为收缩的阿贝尔理想。当抛物子代数𝔭的莱维因子关于反对角线分解为三个对称块时，本文证明，与𝔭的典范截断的收缩相关的对称不变量代数是多项式代数，我们可以给出代数独立齐次生成元的数量、它们的权和次数。该方法依赖于为此类收缩构造适配对（adapted pair）。作为副产品，我们得到，当中心块与莱维因子的两个极端块大小不同时，与A型中此类抛物子代数𝔭的伊诺尼-维格纳收缩相关的对称半不变量生成的代数具有魏尔斯特拉斯截面（Weierstrass section），因此是多项式代数。
英文摘要
This paper deals with polynomiality of algebras of symmetric invariants (or generated by symmetric semi-invariants) associated with some particular Inönü-Wigner contractions in type A. More precisely we are interested with contractions of some parabolic subalgebras in type A with respect to their decomposition into their Levi factor and their nilpotent radical, the latter becoming an abelian ideal of the contraction. When the parabolic subalgebra $\mathfrak p$ has its Levi factor decomposing into three symmetric blocks, with respect to the antidiagonal, we show in this article that the algebra of symmetric invariants associated with the contraction of the canonical truncation of $\mathfrak p$ is a polynomial algebra, for which we can give the number of algebraically independent homogeneous generators, their weight and degree. The method relies on the construction of an adapted pair for such a contraction. As a by-product we obtain that the algebra generated by symmetric semi-invariants associated with the Inönü-Wigner contraction of such a parabolic subalgebra $\mathfrak p$ in type A has a Weierstrass section and then is a polynomial algebra, when the central block is not of the same size as the two extremal blocks of the Levi factor.
Comments44 pages. 2 Figures
