论文标题
线性差分运算符的符号的不变性
Invariants of symbols of the linear differential operators
论文作者
论文摘要
在本文中，我们将$ k $的线性差分运算符的符号分类为$ k $的符号，这些符号从模块$ c^\ infty（ξ）$作用于模块$ c^\ infty（蒜 $E^*:=\mathrm{Hom}(E,\mathbb{C})$ or $ξ^\flat$ with fiber $E^\flat:=\mathrm{Hom}(E, Λ^n T^*)$ and $C^\infty(ξ)$, $C^\infty(ξ^t)$ are the modules of their smooth sections.为了找到与每个非脱生符号相关联的符号的不变性，该符号是在空间$ e $上作用的线性操作员的元组，并将我们的问题减少到与某些正交转换相对于此类元组的分类。使用C. procesi的结果，我们找到了符号的理性不变式领域的生成器，就这些不变性而言，我们提供了相当于非分离符号的标准。
In this paper we classify the symbols of the linear differential operators of order $k$, which act from the module $C^\infty(ξ)$ to the module $C^\infty(ξ^t)$, where $ξ\colon E(ξ)\to M$ is vector bundle over the smooth manifold $M$, bundle $ξ^t$ is either $ξ^*$ with fiber $E^*:=\mathrm{Hom}(E,\mathbb{C})$ or $ξ^\flat$ with fiber $E^\flat:=\mathrm{Hom}(E, Λ^n T^*)$ and $C^\infty(ξ)$, $C^\infty(ξ^t)$ are the modules of their smooth sections. To find invariants of the symbols we associate with every non-degenerated symbol the tuple of linear operators acting on space $E$ and reduce our problem to the classification of such tuples with respect to some orthogonal transformations. Using the results of C. Procesi, we find generators for the field of rational invariants of the symbols and in terms of these invariants provide a criterion of equivalence of non-degenerated symbols.
