A class of Baker-Akhiezer arrangements

Feigin, M. and Johnston, D. (2014) A class of Baker-Akhiezer arrangements. Communications in Mathematical Physics, 328(3), pp. 1117-1157. (doi: 10.1007/s00220-014-1921-4)

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Publisher's URL: http://dx.doi.org/10.1007/s00220-014-1921-4


We study a class of arrangements of lines with multiplicities on the plane which admit the Chalykh–Veselov Baker–Akhiezer function. These arrangements are obtained by adding multiplicity one lines in an invariant way to any dihedral arrangement with invariant multiplicities. We describe all the Baker–Akhiezer arrangements when at most one line has multiplicity higher than 1. We study associated algebras of quasi-invariants which are isomorphic to the commutative algebras of quantum integrals for the generalized Calogero–Moser operators. We compute the Hilbert series of these algebras and we conclude that the algebras are Gorenstein. We also show that there are no other arrangements with Gorenstein algebras of quasi-invariants when at most one line has multiplicity bigger than 1.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Johnston, Mr David and Feigin, Professor Misha
Authors: Feigin, M., and Johnston, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
ISSN (Online):1432-0916
Copyright Holders:Copyright © 2014 The Authors
First Published:First published in Communications in Mathematical Physics 328(3): 1117-1157
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
468861Calogero-Moser systems, Cherednik algebras and Frobenius structuresMikhail FeiginEngineering & Physical Sciences Research Council (EPSRC)EP/F032889/1M&S - MATHEMATICS