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arXiv · 1703.01762

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

Igor Burban·Alexander Zheglov
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Abstract

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.

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Igor Burban, Alexander Zheglov. 2017-03-06. Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems. https://doi.org/10.1112/plms.12341

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