Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems

Autor:	Burban, Igor, Zheglov, Alexander
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Geometry Mathematical Physics Mathematics - Representation Theory
Druh dokumentu:	Working Paper
DOI:	10.1112/plms.12341
Popis:	In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen-Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen-Macaulay modules of rank one over them and determine their Picard groups. In terms of this classification, we describe the spectral modules of the planar rational Calogero-Moser systems. Finally, we elaborate the theory of the algebraic inverse scattering method, computing a new unexpected explicit example of a deformed Calogero-Moser system. Comment: 50 pages, some misprints corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.01762 Zobrazit plný text záznamu View this record from Arxiv