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

Kohei Motegi, Kazumitsu Sakai, Satoshi Watanabe

Research output: Contribution to journalArticle

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 languageEnglish
Article number103571
JournalJournal of Geometry and Physics
Volume149
DOIs
Publication statusPublished - Mar 2020

Fingerprint

Whittaker functions
Whittaker Function
Schur Functions
Inverse Scattering
inverse scattering
Partition Function
partitions
ice
Correspondence
Domain Wall
Generalized Functions
Model
Cauchy
domain wall
Generalization

Keywords

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

Cite this

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

In: Journal of Geometry and Physics, Vol. 149, 103571, 03.2020.

Research output: Contribution to journalArticle

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