关于Coxeter群的m-拟不变量
On m-quasiinvariants of Coxeter groups
摘要：
设W是欧氏向量空间V中的有限Coxeter群，m是W中反射集上的W不变Z+值函数. Chalyh和Veselov引入了一个有趣的代数Q_m，称之为W的m-拟不变量代数。这是具有耦合常数m的有理Calogero-Moser系统的量子积分代数。Feigin和Veselov在最近的一篇论文math-ph/0105014中提出了一些关于Q_m结构的有趣的推论，并对二面体群和常数函数m进行了验证。我们的目标是在一般情况下证明其中的一些定理。
英文摘要：
Let W be a finite Coxeter group in a Euclidean vector space V, and m a W-invariant Z_+-valued function on the set of reflections in W. Chalyh and Veselov introduced in an interesting algebra Q_m, called the algebra of m-quasiinvariants for W. This is the algebra of quantum integrals of the rational Calogero-Moser system with coupling constants m. In a recent paper math-ph/0105014, Feigin and Veselov proposed a number of interesting conjectures concerning the structure of Q_m, and verified them for dihedral groups and constant functions m. Our goal is to prove some of these conjectures in the general case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
