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Matrix product solution to the reflection equation associated with a coideal subalgebra of \(\varvec{U_q(A^{(1)}_{n-1})}\)

  • Atsuo KunibaEmail author
  • Masato Okado
  • Akihito Yoneyama
Article
  • 25 Downloads

Abstract

We present a new solution to the reflection equation associated with a coideal subalgebra of \(U_q(A^{(1)}_{n-1})\) in the symmetric tensor representations and their dual. Elements of the K matrix are expressed by a matrix product formula involving terminating q-hypergeometric series in q-boson generators. At \(q=0\), our result reproduces a known set-theoretical solution to the reflection equation connected to the crystal base theory.

Keywords

Quantum groups Reflection equation Coideal subalgebra Onsager algebra Matrix product method 

Mathematics Subject Classification

Primary 17B37 Secondary 17B80 

Notes

Acknowledgements

The authors thank Vladimir Mangazeev, Zengo Tsuboi and Bart Vlaar for comments. A.K. is supported by Grants-in-Aid for Scientific Research No. 18H01141 from JSPS. M.O. is supported by Grants-in-Aid for Scientific Research No. 15K13429 and No. 16H03922 from JSPS.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of TokyoTokyoJapan
  2. 2.Department of MathematicsOsaka City UniversityOsakaJapan

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