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Representations of quantum superalgebra U q [gl(2|1)] in a coherent state basis and generalization
The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum super...
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Published in: | Journal of mathematical physics 2011-12, Vol.52 (12), p.123512-123512-12 |
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container_end_page | 123512-12 |
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container_title | Journal of mathematical physics |
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creator | Kien, Nguyen Cong Ky, Nguyen Anh Nam, Le Ba Van, Nguyen Thi Hong |
description | The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except U
q
[osp(1|2)], one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely U
q
[gl(2|1)], in constructing q–boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of q–boson-fermion realizations and finite-dimensional representations of U
q
[gl(2|1)] and, thus, at q = 1, of gl(2|1). Both gl(2|1) and U
q
[gl(2|1)] have found different physics applications, therefore, it is meaningful to construct their representations. |
doi_str_mv | 10.1063/1.3671330 |
format | article |
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q
[osp(1|2)], one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely U
q
[gl(2|1)], in constructing q–boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of q–boson-fermion realizations and finite-dimensional representations of U
q
[gl(2|1)] and, thus, at q = 1, of gl(2|1). Both gl(2|1) and U
q
[gl(2|1)] have found different physics applications, therefore, it is meaningful to construct their representations.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.3671330</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>American Institute of Physics</publisher><ispartof>Journal of mathematical physics, 2011-12, Vol.52 (12), p.123512-123512-12</ispartof><rights>American Institute of Physics</rights><rights>2011 American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-132474e2323d475ac4993bce6722ec2f85ec0c70f507f249668648afdbc99b0a3</citedby><cites>FETCH-LOGICAL-c354t-132474e2323d475ac4993bce6722ec2f85ec0c70f507f249668648afdbc99b0a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.3671330$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,782,784,795,27924,27925,76383</link.rule.ids></links><search><creatorcontrib>Kien, Nguyen Cong</creatorcontrib><creatorcontrib>Ky, Nguyen Anh</creatorcontrib><creatorcontrib>Nam, Le Ba</creatorcontrib><creatorcontrib>Van, Nguyen Thi Hong</creatorcontrib><title>Representations of quantum superalgebra U q [gl(2|1)] in a coherent state basis and generalization</title><title>Journal of mathematical physics</title><description>The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except U
q
[osp(1|2)], one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely U
q
[gl(2|1)], in constructing q–boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of q–boson-fermion realizations and finite-dimensional representations of U
q
[gl(2|1)] and, thus, at q = 1, of gl(2|1). Both gl(2|1) and U
q
[gl(2|1)] have found different physics applications, therefore, it is meaningful to construct their representations.</description><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kF1LwzAYRoMoOKcX_oNcOqEzX03SG0HG_ICBIO5KJKTpm1nZ2i7pBMUfb-cGgjKvcnPO4c2D0CklQ0okv6BDLhXlnOyhHiU6S5RM9T7qEcJYwoTWh-goxldCKNVC9FD-AE2ACFVr27KuIq49Xq5s1a4WOK4aCHY-gzxYPMVL_DSbn7FPOnjGZYUtdvULhM7EsZMB5zaWEduqwDOo1mL58d08RgfeziOcbN8-ml6PH0e3yeT-5m50NUkcT0WbUM6EEsA444VQqXUiy3juQCrGwDGvU3DEKeJTojwTmZRaCm19kbssy4nlfTTYdF2oYwzgTRPKhQ3vhhKzHsdQsx2nYy83bHTl5ue74V8LmdqbZRc43xV4q8OPbJrC_wf_Pe0LSbiI0Q</recordid><startdate>20111201</startdate><enddate>20111201</enddate><creator>Kien, Nguyen Cong</creator><creator>Ky, Nguyen Anh</creator><creator>Nam, Le Ba</creator><creator>Van, Nguyen Thi Hong</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20111201</creationdate><title>Representations of quantum superalgebra U q [gl(2|1)] in a coherent state basis and generalization</title><author>Kien, Nguyen Cong ; Ky, Nguyen Anh ; Nam, Le Ba ; Van, Nguyen Thi Hong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-132474e2323d475ac4993bce6722ec2f85ec0c70f507f249668648afdbc99b0a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kien, Nguyen Cong</creatorcontrib><creatorcontrib>Ky, Nguyen Anh</creatorcontrib><creatorcontrib>Nam, Le Ba</creatorcontrib><creatorcontrib>Van, Nguyen Thi Hong</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kien, Nguyen Cong</au><au>Ky, Nguyen Anh</au><au>Nam, Le Ba</au><au>Van, Nguyen Thi Hong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Representations of quantum superalgebra U q [gl(2|1)] in a coherent state basis and generalization</atitle><jtitle>Journal of mathematical physics</jtitle><date>2011-12-01</date><risdate>2011</risdate><volume>52</volume><issue>12</issue><spage>123512</spage><epage>123512-12</epage><pages>123512-123512-12</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except U
q
[osp(1|2)], one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely U
q
[gl(2|1)], in constructing q–boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of q–boson-fermion realizations and finite-dimensional representations of U
q
[gl(2|1)] and, thus, at q = 1, of gl(2|1). Both gl(2|1) and U
q
[gl(2|1)] have found different physics applications, therefore, it is meaningful to construct their representations.</abstract><pub>American Institute of Physics</pub><doi>10.1063/1.3671330</doi><tpages>12</tpages></addata></record> |
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title | Representations of quantum superalgebra U q [gl(2|1)] in a coherent state basis and generalization |
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