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Baxter q-operators and representations of yangians

Bazhanov, Vladimir; Frassek, Rouven; Lukowski, Tomasz; Meneghelli, Carlo; Staudacher, Matthias

Description

We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we...[Show more]

dc.contributor.authorBazhanov, Vladimir
dc.contributor.authorFrassek, Rouven
dc.contributor.authorLukowski, Tomasz
dc.contributor.authorMeneghelli, Carlo
dc.contributor.authorStaudacher, Matthias
dc.date.accessioned2015-12-10T23:32:19Z
dc.identifier.issn0550-3213
dc.identifier.urihttp://hdl.handle.net/1885/68789
dc.description.abstractWe develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider gl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe Ansatz techniques.
dc.publisherElsevier
dc.rightsAuthor/s retain copyright
dc.sourceNuclear Physics B
dc.titleBaxter q-operators and representations of yangians
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume850
dc.date.issued2011
local.identifier.absfor010502 - Integrable Systems (Classical and Quantum)
local.identifier.ariespublicationf2965xPUB1830
local.type.statusPublished Version
local.contributor.affiliationBazhanov, Vladimir, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationFrassek, Rouven, Humboldt-Universit├Ąt zu Berlin
local.contributor.affiliationLukowski, Tomasz, Jagellonian University
local.contributor.affiliationMeneghelli, Carlo, Albert-Einstein-Institut
local.contributor.affiliationStaudacher, Matthias, Albert-Einstein-Institut
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage148
local.bibliographicCitation.lastpage174
local.identifier.doi10.1016/j.nuclphysb.2011.04.006
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.absseo970102 - Expanding Knowledge in the Physical Sciences
dc.date.updated2015-12-10T11:18:51Z
local.identifier.scopusID2-s2.0-79957491141
local.identifier.thomsonID000292409600005
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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