Letters in Mathematical Physics

, Volume 109, Issue 4, pp 923–943 | Cite as

Elliptic free-fermion model with OS boundary and elliptic Pfaffians

  • Kohei MotegiEmail author


We introduce and study a class of partition functions of an elliptic free-fermionic face model. We study the partition functions with a triangular boundary using the off-diagonal K-matrix at the boundary (OS boundary), which was introduced by Kuperberg as a class of variants of the domain wall boundary partition functions. We find explicit forms of the partition functions with OS boundary using elliptic Pfaffians. We find two expressions based on two versions of Korepin’s method, and we obtain an identity between two elliptic Pfaffians as a corollary.


Elliptic integrable models Partition functions Yang-Baxter equation Elliptic Pfaffians 

Mathematics Subject Classification

33E05 16T25 16T30 82B23 



The author thanks the referees for careful reading, various invaluable comments and suggestions to improve the paper. This work was partially supported by Grant-in-Aid for Scientific Research (C) No. 18K03205 and No. 16K05468.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Faculty of Marine TechnologyTokyo University of Marine Science and TechnologyTokyoJapan

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