论文标题
Noether问题的泊松类似物
A Poisson Analogue of Noether's Problem
论文作者
论文摘要
在本文中，我们表明，Noether问题的泊松类似物对所有有限的符号反射群都有一个积极的解决方案，即同时世界中复杂反射组的类似物。我们的证明是建设性的，并概括并完善了先前已知的结果。作为对复杂反射组的解决方案解决方案的有趣结果，我们获得了与任何复杂反射组相关的Calogero-Moser空间的泊松合理性。可以将本文的结果视为非公共性问题的类似物，而Gelfand-kirillov猜想是“准经典限制”中理性Cherednik代数的类似物。在本文的后半部分，引入了一个抽象的框架，以了解这些结果，并显示出$ 3D \，\ Mathcal {n} = 4 $ gauge理论的每个Coloumb分支都是Poisson Rational作为应用程序。我们还获得了三角cherednik代数的Gelfand-Kirillov猜想，并同时获得了其三角calogero-Moser空间的泊松合理性。
In this paper we show that the Poisson analogue of the Noether's Problem has a positive solution for essentially all finite symplectic reflection groups - the analogue of complex reflection groups in the symplectic world. Our proofs are constructive, and generalize and refines previously known results. As an interesting consequence of the solution of this problem for complex reflection groups, we obtain the Poisson rationality of the Calogero-Moser spaces associated to any complex reflection group. The results of this paper can be thought as analogues of the Noncommutative Noether Problem and the Gelfand-Kirillov Conjecture for rational Cherednik algebras in the 'quasi-classical limit'. In the second half of the paper, an abstract framework to understand these results is introduced, and it is shown that every Coloumb branch of a $3d \, \mathcal{N}=4$ gauge theory is Poisson rational as an application. We also obtain the Gelfand-Kirillov Conjecture for trigonometric Cherednik algebras and the Poisson rationality of their trigonometric Calogero-Moser spaces at the same time.
