Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-11
Main Authors: van Diejen, J F, Emsiz, E, Zurrián, I N
Format: Article
Language:English
Subjects:
Eigenvectors
Integrals
Mathematical analysis
Polynomials
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator van Diejen, J F
Emsiz, E
Zurrián, I N
description We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.
doi_str_mv 10.48550/arxiv.1611.05922
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2071989201</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2071989201</sourcerecordid><originalsourceid>FETCH-proquest_journals_20719892013</originalsourceid><addsrcrecordid>eNqNisFOwkAQhjcmJhLlAbxN4gUPrbtTFtojEgwP4JGEbHUqJWWm7GxVfHrR-ABe_i_5vt-YW2fzaem9fQjxs33P3cy53PoK8cKMsChcVk4Rr8xYdW-txdkcvS9GhpZy6DtKxKQK0kDaETzSzy5YQ_qCRiIEBumJYTM5bu6zWlQY9KSJDvDRph20nOgthrojqGXg1xBPvy6Gl9QK6425bEKnNP7jtbl7Wj0v11kf5TiQpu1ehsjntEU7d1VZoXXF_17fBL1M7A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2071989201</pqid></control><display><type>article</type><title>Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions</title><source>Publicly Available Content (ProQuest)</source><creator>van Diejen, J F ; Emsiz, E ; Zurrián, I N</creator><creatorcontrib>van Diejen, J F ; Emsiz, E ; Zurrián, I N</creatorcontrib><description>We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1611.05922</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Eigenvectors ; Integrals ; Mathematical analysis ; Polynomials</subject><ispartof>arXiv.org, 2016-11</ispartof><rights>2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2071989201?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25752,27924,37011,44589</link.rule.ids></links><search><creatorcontrib>van Diejen, J F</creatorcontrib><creatorcontrib>Emsiz, E</creatorcontrib><creatorcontrib>Zurrián, I N</creatorcontrib><title>Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions</title><title>arXiv.org</title><description>We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.</description><subject>Eigenvectors</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Polynomials</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNisFOwkAQhjcmJhLlAbxN4gUPrbtTFtojEgwP4JGEbHUqJWWm7GxVfHrR-ABe_i_5vt-YW2fzaem9fQjxs33P3cy53PoK8cKMsChcVk4Rr8xYdW-txdkcvS9GhpZy6DtKxKQK0kDaETzSzy5YQ_qCRiIEBumJYTM5bu6zWlQY9KSJDvDRph20nOgthrojqGXg1xBPvy6Gl9QK6425bEKnNP7jtbl7Wj0v11kf5TiQpu1ehsjntEU7d1VZoXXF_17fBL1M7A</recordid><startdate>20161117</startdate><enddate>20161117</enddate><creator>van Diejen, J F</creator><creator>Emsiz, E</creator><creator>Zurrián, I N</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20161117</creationdate><title>Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions</title><author>van Diejen, J F ; Emsiz, E ; Zurrián, I N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20719892013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Eigenvectors</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Polynomials</topic><toplevel>online_resources</toplevel><creatorcontrib>van Diejen, J F</creatorcontrib><creatorcontrib>Emsiz, E</creatorcontrib><creatorcontrib>Zurrián, I N</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>van Diejen, J F</au><au>Emsiz, E</au><au>Zurrián, I N</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions</atitle><jtitle>arXiv.org</jtitle><date>2016-11-17</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1611.05922</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2016-11
issn 2331-8422
language eng
recordid cdi_proquest_journals_2071989201
source Publicly Available Content (ProQuest)
subjects Eigenvectors
Integrals
Mathematical analysis
Polynomials
title Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-09T06%3A33%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Completeness%20of%20the%20Bethe%20Ansatz%20for%20an%20open%20%5C(q%5C)-boson%20system%20with%20integrable%20boundary%20interactions&rft.jtitle=arXiv.org&rft.au=van%20Diejen,%20J%20F&rft.date=2016-11-17&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1611.05922&rft_dat=%3Cproquest%3E2071989201%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20719892013%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2071989201&rft_id=info:pmid/&rfr_iscdi=true