Young diagrams in an N × M box and the KP hierarchy
In this paper, we firstly find that the multiplications HM(u1)HM(u2)⋯HM(uN) are tau functions of the KP hierarchy for any positive integer numbers M,N, where HM(z) is the generating function of Young diagrams in an 1×M box. Then as applications, we find that the general states and the scalar product...
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| Format: | Article |
| Language: | English |
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Elsevier
2018-12-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321318303006 |
| _version_ | 1818910901690957824 |
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| author | Na Wang |
| author_facet | Na Wang |
| author_sort | Na Wang |
| collection | DOAJ |
| description | In this paper, we firstly find that the multiplications HM(u1)HM(u2)⋯HM(uN) are tau functions of the KP hierarchy for any positive integer numbers M,N, where HM(z) is the generating function of Young diagrams in an 1×M box. Then as applications, we find that the general states and the scalar products of general states in the phase model and the XX0 model are all tau functions of the KP hierarchy. We also discuss the wave functions in these models. |
| first_indexed | 2024-12-19T22:50:10Z |
| format | Article |
| id | doaj.art-329298ad34564ca29dc349898f9d2831 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-19T22:50:10Z |
| publishDate | 2018-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-329298ad34564ca29dc349898f9d28312022-12-21T20:02:49ZengElsevierNuclear Physics B0550-32132018-12-01937478501Young diagrams in an N × M box and the KP hierarchyNa Wang0Department of Mathematics and Statistics, Henan University, Kaifeng, 475001, ChinaIn this paper, we firstly find that the multiplications HM(u1)HM(u2)⋯HM(uN) are tau functions of the KP hierarchy for any positive integer numbers M,N, where HM(z) is the generating function of Young diagrams in an 1×M box. Then as applications, we find that the general states and the scalar products of general states in the phase model and the XX0 model are all tau functions of the KP hierarchy. We also discuss the wave functions in these models.http://www.sciencedirect.com/science/article/pii/S0550321318303006 |
| spellingShingle | Na Wang Young diagrams in an N × M box and the KP hierarchy Nuclear Physics B |
| title | Young diagrams in an N × M box and the KP hierarchy |
| title_full | Young diagrams in an N × M box and the KP hierarchy |
| title_fullStr | Young diagrams in an N × M box and the KP hierarchy |
| title_full_unstemmed | Young diagrams in an N × M box and the KP hierarchy |
| title_short | Young diagrams in an N × M box and the KP hierarchy |
| title_sort | young diagrams in an n m box and the kp hierarchy |
| url | http://www.sciencedirect.com/science/article/pii/S0550321318303006 |
| work_keys_str_mv | AT nawang youngdiagramsinannmboxandthekphierarchy |