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### Norm formulae for the Bethe Ansatz on root systems of small rank

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Bustamante, Miguel D., Van Diejen, Jan Felipe and de la Maza, A. C..
(2008)
*Norm formulae for the Bethe Ansatz on root systems of small rank.*
Journal of Physics A: Mathematical and Theoretical, Volume 41
(Number 2).
Article No. 025202.
ISSN 1751-8113

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1088/1751-8113/41/2/025202

## Abstract

The norms of the Bethe Ansatz eigenfunctions for the Lieb-Liniger quantum system of n Bosonic particles on a ring with pairwise repulsive delta potential interactions are given by a beautiful determinantal formula, first conjectured by Gaudin in the early seventies and then proven by Korepin about a decade later. Recently, E Emsiz formulated a similar conjecture generalizing the Gaudin-Korepin norm formula in terms of the root systems of complex simple Lie algebras. Here we confirm the validity of the conjecture in question for small root systems up to rank 3 ( thus including the important test case of the exceptional root system G(2)).

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Bethe-ansatz technique, Root systems (Algebra), Eigenfunctions |

Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical |

Publisher: | IOP Publishing Ltd |

ISSN: | 1751-8113 |

Official Date: | 18 January 2008 |

Volume: | Volume 41 |

Number: | Number 2 |

Number of Pages: | 13 |

Page Range: | Article No. 025202 |

Identification Number: | 10.1088/1751-8113/41/2/025202 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | Fondo Nacional de Desarrollo Científico y Tecnológico (Chile) (FONDECYT), World Bank, Universidad de Talca |

Grant number: | 1051012, 1040896 (FONDECYT) |

References: | [B] Bourbaki N 1968 Groupes et alg`ebres de Lie (Paris: Hermann) chapitres 4–6 |

URI: | http://wrap.warwick.ac.uk/id/eprint/30623 |

Data sourced from Thomson Reuters' Web of Knowledge

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