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dc.contributor.authorRains, Eric
dc.contributor.authorEtingof, Pavel I
dc.date.accessioned2017-03-04T00:18:18Z
dc.date.available2017-03-04T00:18:18Z
dc.date.issued2016-05
dc.date.submitted2015-07
dc.identifier.issn0010-3616
dc.identifier.issn1432-0916
dc.identifier.urihttp://hdl.handle.net/1721.1/107184
dc.description.abstractGeneralized power sums are linear combinations of ith powers of coordinates. We consider subalgebras of the polynomial algebra generated by generalized power sums, and study when such algebras are Cohen–Macaulay. It turns out that the Cohen–Macaulay property of such algebras is rare, and tends to be related to quantum integrability and representation theory of Cherednik algebras. Using representation theoretic results and deformation theory, we establish Cohen–Macaulayness of the algebra of q, t-deformed power sums defined by Sergeev and Veselov, and of some generalizations of this algebra, proving a conjecture of Brookner, Corwin, Etingof, and Sam. We also apply representation-theoretic techniques to studying m-quasi-invariants of deformed Calogero–Moser systems. In an appendix to this paper, M. Feigin uses representation theory of Cherednik algebras to compute Hilbert series for such quasi-invariants, and show that in the case of one light particle, the ring of quasi-invariants is Gorenstein.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant DMS-1000113)en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00220-016-2657-0en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleOn Cohen–Macaulayness of Algebras Generated by Generalized Power Sumsen_US
dc.typeArticleen_US
dc.identifier.citationEtingof, Pavel, and Eric Rains. “On Cohen–Macaulayness of Algebras Generated by Generalized Power Sums.” Communications in Mathematical Physics 347, no. 1 (May 26, 2016): 163–182.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorEtingof, Pavel I
dc.relation.journalCommunications in Mathematical Physicsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2017-02-02T15:20:13Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag Berlin Heidelberg
dspace.orderedauthorsEtingof, Pavel; Rains, Ericen_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0002-0710-1416
mit.licenseOPEN_ACCESS_POLICYen_US


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