Poisson No ether's Problem and Poisson rationality

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Author(s):	Schwarz, Joao Total Authors: 1
Document type:	Journal article
Source:	Journal of Algebra; v. 606, p. 14-pg., 2022-05-20.
Abstract
In this paper we show that the Poisson analogue of the No ether's Problem has a positive solution for essentially all symplectic reflection groups - the analogue of complex reflection groups in the symplectic world. Our proofs are constructive, and generalize and refine previously known results. 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. An abstract framework to understand these results is introduced. As a consequence for complex reflection groups, we obtain the Poisson rationality of the Calogero-Moser spaces associated to any of them, and we verify the Gelfand-Kirillov Conjecture for trigonometric Cherednik algebras and the Poisson rationality of their corresponding Calogero-Moser spaces. (AU)

FAPESP's process:	18/18146-5 - Ore Domainas: localizations, invariants and representations.
Grantee:	João Fernando Schwarz
Support Opportunities:	Scholarships in Brazil - Post-Doctoral