### Abstract

We introduce generalizations of type C and B ice models which were recently introduced by Ivanov and Brubaker–Bump–Chinta–Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering method. We compute the explicit forms of the wavefunctions and their duals by using the Izergin–Korepin technique, which can be applied to both models. For type C ice, we show the wavefunctions are expressed using generalizations of the symplectic Schur functions. This gives a generalization of the correspondence by Ivanov. For type B ice, we prove that the exact expressions of the wavefunctions are given by generalizations of the Whittaker functions introduced by Bump–Friedberg–Hoffstein. The special case is the correspondence conjectured by Brubaker–Bump–Chinta–Gunnells. We also show the factorized forms for the domain wall boundary partition functions for both models. As a consequence of the studies of the partition functions, we obtain dual Cauchy formulas for the generalized symplectic Schur functions and the generalized Whittaker functions.

Original language | English |
---|---|

Article number | 103571 |

Journal | Journal of Geometry and Physics |

Volume | 149 |

DOIs | |

Publication status | Published - Mar 2020 |

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### Keywords

- Quantum dynamical and integrable systems
- Quantum groups
- Quantum integrable models
- Representation theory
- Symmetric functions
- Whittaker functions

### Cite this

*Journal of Geometry and Physics*,

*149*, [103571]. https://doi.org/10.1016/j.geomphys.2019.103571

}

*Journal of Geometry and Physics*, vol. 149, 103571. https://doi.org/10.1016/j.geomphys.2019.103571

**Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions.** / Motegi, Kohei; Sakai, Kazumitsu; Watanabe, Satoshi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions

AU - Motegi, Kohei

AU - Sakai, Kazumitsu

AU - Watanabe, Satoshi

PY - 2020/3

Y1 - 2020/3

N2 - We introduce generalizations of type C and B ice models which were recently introduced by Ivanov and Brubaker–Bump–Chinta–Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering method. We compute the explicit forms of the wavefunctions and their duals by using the Izergin–Korepin technique, which can be applied to both models. For type C ice, we show the wavefunctions are expressed using generalizations of the symplectic Schur functions. This gives a generalization of the correspondence by Ivanov. For type B ice, we prove that the exact expressions of the wavefunctions are given by generalizations of the Whittaker functions introduced by Bump–Friedberg–Hoffstein. The special case is the correspondence conjectured by Brubaker–Bump–Chinta–Gunnells. We also show the factorized forms for the domain wall boundary partition functions for both models. As a consequence of the studies of the partition functions, we obtain dual Cauchy formulas for the generalized symplectic Schur functions and the generalized Whittaker functions.

AB - We introduce generalizations of type C and B ice models which were recently introduced by Ivanov and Brubaker–Bump–Chinta–Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering method. We compute the explicit forms of the wavefunctions and their duals by using the Izergin–Korepin technique, which can be applied to both models. For type C ice, we show the wavefunctions are expressed using generalizations of the symplectic Schur functions. This gives a generalization of the correspondence by Ivanov. For type B ice, we prove that the exact expressions of the wavefunctions are given by generalizations of the Whittaker functions introduced by Bump–Friedberg–Hoffstein. The special case is the correspondence conjectured by Brubaker–Bump–Chinta–Gunnells. We also show the factorized forms for the domain wall boundary partition functions for both models. As a consequence of the studies of the partition functions, we obtain dual Cauchy formulas for the generalized symplectic Schur functions and the generalized Whittaker functions.

KW - Quantum dynamical and integrable systems

KW - Quantum groups

KW - Quantum integrable models

KW - Representation theory

KW - Symmetric functions

KW - Whittaker functions

UR - http://www.scopus.com/inward/record.url?scp=85076733174&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2019.103571

DO - 10.1016/j.geomphys.2019.103571

M3 - Article

AN - SCOPUS:85076733174

VL - 149

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

M1 - 103571

ER -