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
Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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 |
Publisher: | Springer-Verlag |
ISSN: | 0010-3616 |
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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