Polynomial ring representations of endomorphisms of exterior powers
An explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k -th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning t...
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| Veröffentlicht in: | Collectanea mathematica (Barcelona) 2022, Vol.73 (1), p.107-133 |
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| container_title | Collectanea mathematica (Barcelona) |
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| creator | Behzad, Ommolbanin Contiero, André Gatto, Letterio Martins, Renato Vidal |
| description | An explicit description of the ring of the rational polynomials in
r
indeterminates as a representation of the Lie algebra of the endomorphisms of the
k
-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many. |
| doi_str_mv | 10.1007/s13348-020-00310-5 |
| format | Article |
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r
indeterminates as a representation of the Lie algebra of the endomorphisms of the
k
-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.</description><identifier>ISSN: 0010-0757</identifier><identifier>EISSN: 2038-4815</identifier><identifier>DOI: 10.1007/s13348-020-00310-5</identifier><language>eng</language><publisher>Milan: Springer Milan</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Lie groups ; Mathematics ; Mathematics and Statistics ; Matrix algebra ; Operators (mathematics) ; Polynomials ; Representations ; Rings (mathematics)</subject><ispartof>Collectanea mathematica (Barcelona), 2022, Vol.73 (1), p.107-133</ispartof><rights>The Author(s) 2021</rights><rights>The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-f2b3695afb19fd7c40e61c2b8f21e9027bb0a51aa7a295f2ea4367e83bc128323</citedby><cites>FETCH-LOGICAL-c363t-f2b3695afb19fd7c40e61c2b8f21e9027bb0a51aa7a295f2ea4367e83bc128323</cites><orcidid>0000-0002-3446-2663</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13348-020-00310-5$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13348-020-00310-5$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,778,782,27911,27912,41475,42544,51306</link.rule.ids></links><search><creatorcontrib>Behzad, Ommolbanin</creatorcontrib><creatorcontrib>Contiero, André</creatorcontrib><creatorcontrib>Gatto, Letterio</creatorcontrib><creatorcontrib>Martins, Renato Vidal</creatorcontrib><title>Polynomial ring representations of endomorphisms of exterior powers</title><title>Collectanea mathematica (Barcelona)</title><addtitle>Collect. Math</addtitle><description>An explicit description of the ring of the rational polynomials in
r
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k
-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Lie groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix algebra</subject><subject>Operators (mathematics)</subject><subject>Polynomials</subject><subject>Representations</subject><subject>Rings (mathematics)</subject><issn>0010-0757</issn><issn>2038-4815</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEFLw0AQhRdRsFb_gKeA59WZ3SSbHKWoFQp60POySWc1pcnG2RTtvzc1gjdPA4_3vYFPiEuEawQwNxG1TgsJCiSARpDZkZgp0IVMC8yOxQxgDMFk5lScxbgBSBWimYnFc9juu9A2bptw070lTD1TpG5wQxO6mASfULcObeD-vYntFHwNxE3gpA-fxPFcnHi3jXTxe-fi9f7uZbGUq6eHx8XtStY614P0qtJ5mTlfYenXpk6BcqxVVXiFVIIyVQUuQ-eMU2XmFblU54YKXdWoCq30XFxNuz2Hjx3FwW7CjrvxpVU55tqYskzHlppaNYcYmbztuWkd7y2CPciykyw7yrI_smw2QnqCYn-wQPw3_Q_1DZalbSw</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Behzad, Ommolbanin</creator><creator>Contiero, André</creator><creator>Gatto, Letterio</creator><creator>Martins, Renato Vidal</creator><general>Springer Milan</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3446-2663</orcidid></search><sort><creationdate>2022</creationdate><title>Polynomial ring representations of endomorphisms of exterior powers</title><author>Behzad, Ommolbanin ; Contiero, André ; Gatto, Letterio ; Martins, Renato Vidal</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-f2b3695afb19fd7c40e61c2b8f21e9027bb0a51aa7a295f2ea4367e83bc128323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Lie groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix algebra</topic><topic>Operators (mathematics)</topic><topic>Polynomials</topic><topic>Representations</topic><topic>Rings (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Behzad, Ommolbanin</creatorcontrib><creatorcontrib>Contiero, André</creatorcontrib><creatorcontrib>Gatto, Letterio</creatorcontrib><creatorcontrib>Martins, Renato Vidal</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Collectanea mathematica (Barcelona)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Behzad, Ommolbanin</au><au>Contiero, André</au><au>Gatto, Letterio</au><au>Martins, Renato Vidal</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polynomial ring representations of endomorphisms of exterior powers</atitle><jtitle>Collectanea mathematica (Barcelona)</jtitle><stitle>Collect. Math</stitle><date>2022</date><risdate>2022</risdate><volume>73</volume><issue>1</issue><spage>107</spage><epage>133</epage><pages>107-133</pages><issn>0010-0757</issn><eissn>2038-4815</eissn><abstract>An explicit description of the ring of the rational polynomials in
r
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k
-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.</abstract><cop>Milan</cop><pub>Springer Milan</pub><doi>10.1007/s13348-020-00310-5</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0002-3446-2663</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algebra Analysis Applications of Mathematics Geometry Lie groups Mathematics Mathematics and Statistics Matrix algebra Operators (mathematics) Polynomials Representations Rings (mathematics) |
| title | Polynomial ring representations of endomorphisms of exterior powers |
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