An affine Weyl group characterization of polynomial Heisenberg algebras

We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To establish this connection, we employ supersymmetric quantum...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2022-07
1. Verfasser:	Morales-Salgado, V S
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Group theory Harmonic oscillators Mathematical analysis Mathematics - Mathematical Physics Nonlinear differential equations Nonlinear systems Physics - High Energy Physics - Theory Physics - Mathematical Physics Physics - Quantum Physics Polynomials Quantum mechanics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue
container_start_page
container_title	arXiv.org
container_volume
creator	Morales-Salgado, V S
description	We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To establish this connection, we employ supersymmetric quantum mechanics to first connect a polynomial Heisenberg algebra to symmetric systems of differential equations. This connection has been previously used to relate quantum systems to non-linear differential equations; most notably, the fourth and fifth Painlevé equations. Once this is done, we use previous studies on the B\"acklund transformations of Painlevé equations and generalizations of their symmetric forms characterized by extended affine Weyl groups. This work contributes to better understand quantum systems and the algebraic structures characterizing them.
doi_str_mv	10.48550/arxiv.2204.11125
format	Article
fullrecord	<record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_2204_11125</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2655331601</sourcerecordid><originalsourceid>FETCH-LOGICAL-a521-8eae8c3d4c7b94e892487d302ef07a0463178ef24971e444789ad049568e50883</originalsourceid><addsrcrecordid>eNotj0FLwzAYhoMgOOZ-gCcDnleTL0mTHsfQbTDwMvBYvnVfZ0bX1LQV66-3bp7ey8PL8zD2IEWinTHiGeO3_0oAhE6klGBu2ASUknOnAe7YrG1PQghILRijJmy1qDmWpa-Jv9NQ8WMMfcOLD4xYdBT9D3Y-1DyUvAnVUIezx4qvybdU7ykeOVZH2kds79ltiVVLs_-dst3ry265nm_fVpvlYjtHA6MDIblCHXRh95kml4F29qAEUCksCp0qaR2VoDMrSWttXYYHoTOTOjLCOTVlj9fbS2XeRH_GOOR_tfmldiSerkQTw2dPbZefQh_r0SmHdExWMhVS_QKL_lZ5</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2655331601</pqid></control><display><type>article</type><title>An affine Weyl group characterization of polynomial Heisenberg algebras</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Morales-Salgado, V S</creator><creatorcontrib>Morales-Salgado, V S</creatorcontrib><description>We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To establish this connection, we employ supersymmetric quantum mechanics to first connect a polynomial Heisenberg algebra to symmetric systems of differential equations. This connection has been previously used to relate quantum systems to non-linear differential equations; most notably, the fourth and fifth Painlevé equations. Once this is done, we use previous studies on the B\"acklund transformations of Painlevé equations and generalizations of their symmetric forms characterized by extended affine Weyl groups. This work contributes to better understand quantum systems and the algebraic structures characterizing them.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2204.11125</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Group theory ; Harmonic oscillators ; Mathematical analysis ; Mathematics - Mathematical Physics ; Nonlinear differential equations ; Nonlinear systems ; Physics - High Energy Physics - Theory ; Physics - Mathematical Physics ; Physics - Quantum Physics ; Polynomials ; Quantum mechanics</subject><ispartof>arXiv.org, 2022-07</ispartof><rights>2022. 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><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27925</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.2204.11125$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1016/j.aop.2022.169037$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Morales-Salgado, V S</creatorcontrib><title>An affine Weyl group characterization of polynomial Heisenberg algebras</title><title>arXiv.org</title><description>We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To establish this connection, we employ supersymmetric quantum mechanics to first connect a polynomial Heisenberg algebra to symmetric systems of differential equations. This connection has been previously used to relate quantum systems to non-linear differential equations; most notably, the fourth and fifth Painlevé equations. Once this is done, we use previous studies on the B\"acklund transformations of Painlevé equations and generalizations of their symmetric forms characterized by extended affine Weyl groups. This work contributes to better understand quantum systems and the algebraic structures characterizing them.</description><subject>Algebra</subject><subject>Group theory</subject><subject>Harmonic oscillators</subject><subject>Mathematical analysis</subject><subject>Mathematics - Mathematical Physics</subject><subject>Nonlinear differential equations</subject><subject>Nonlinear systems</subject><subject>Physics - High Energy Physics - Theory</subject><subject>Physics - Mathematical Physics</subject><subject>Physics - Quantum Physics</subject><subject>Polynomials</subject><subject>Quantum mechanics</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj0FLwzAYhoMgOOZ-gCcDnleTL0mTHsfQbTDwMvBYvnVfZ0bX1LQV66-3bp7ey8PL8zD2IEWinTHiGeO3_0oAhE6klGBu2ASUknOnAe7YrG1PQghILRijJmy1qDmWpa-Jv9NQ8WMMfcOLD4xYdBT9D3Y-1DyUvAnVUIezx4qvybdU7ykeOVZH2kds79ltiVVLs_-dst3ry265nm_fVpvlYjtHA6MDIblCHXRh95kml4F29qAEUCksCp0qaR2VoDMrSWttXYYHoTOTOjLCOTVlj9fbS2XeRH_GOOR_tfmldiSerkQTw2dPbZefQh_r0SmHdExWMhVS_QKL_lZ5</recordid><startdate>20220711</startdate><enddate>20220711</enddate><creator>Morales-Salgado, V S</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><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220711</creationdate><title>An affine Weyl group characterization of polynomial Heisenberg algebras</title><author>Morales-Salgado, V S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a521-8eae8c3d4c7b94e892487d302ef07a0463178ef24971e444789ad049568e50883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Group theory</topic><topic>Harmonic oscillators</topic><topic>Mathematical analysis</topic><topic>Mathematics - Mathematical Physics</topic><topic>Nonlinear differential equations</topic><topic>Nonlinear systems</topic><topic>Physics - High Energy Physics - Theory</topic><topic>Physics - Mathematical Physics</topic><topic>Physics - Quantum Physics</topic><topic>Polynomials</topic><topic>Quantum mechanics</topic><toplevel>online_resources</toplevel><creatorcontrib>Morales-Salgado, V S</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</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><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Morales-Salgado, V S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An affine Weyl group characterization of polynomial Heisenberg algebras</atitle><jtitle>arXiv.org</jtitle><date>2022-07-11</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type $A^{(1)}_m$, where $m$ is the degree of the PHA. To establish this connection, we employ supersymmetric quantum mechanics to first connect a polynomial Heisenberg algebra to symmetric systems of differential equations. This connection has been previously used to relate quantum systems to non-linear differential equations; most notably, the fourth and fifth Painlevé equations. Once this is done, we use previous studies on the B\"acklund transformations of Painlevé equations and generalizations of their symmetric forms characterized by extended affine Weyl groups. This work contributes to better understand quantum systems and the algebraic structures characterizing them.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2204.11125</doi><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	EISSN: 2331-8422
ispartof	arXiv.org, 2022-07
issn	2331-8422
language	eng
recordid	cdi_arxiv_primary_2204_11125
source	arXiv.org; Free E- Journals
subjects	Algebra Group theory Harmonic oscillators Mathematical analysis Mathematics - Mathematical Physics Nonlinear differential equations Nonlinear systems Physics - High Energy Physics - Theory Physics - Mathematical Physics Physics - Quantum Physics Polynomials Quantum mechanics
title	An affine Weyl group characterization of polynomial Heisenberg algebras
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T16%3A41%3A01IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20affine%20Weyl%20group%20characterization%20of%20polynomial%20Heisenberg%20algebras&rft.jtitle=arXiv.org&rft.au=Morales-Salgado,%20V%20S&rft.date=2022-07-11&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.2204.11125&rft_dat=%3Cproquest_arxiv%3E2655331601%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2655331601&rft_id=info:pmid/&rfr_iscdi=true