Set-theoretic Yang–Baxter & reflection equations and quantum group symmetries

Anastasia Doikou, Agata Smoktunowicz

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12 Citations (Scopus)
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Connections between set-theoretic Yang-Baxter and reflection
equations and quantum integrable systems are investigated. We show that set-theoretic R-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for R-matrices being Baxterized solutions of the A-type Hecke algebra HN (q = 1). We show in the case of the reflection algebra that there exists a “boundary” finite sub-algebra for some special choice of “boundary” elements of the B-type Hecke algebra BN (q = 1, Q). We also show the key proposition that the associated double row transfer matrix is essentially expressed in terms of the elements of the B-type Hecke algebra. This is one of the fundamental results of this investigation together with the
proof of the duality between the boundary finite subalgebra and the B-type Hecke algebra. These are universal statements that largely generalize previous relevant findings, and also allow the investigation of the symmetries of the double row transfer matrix.
Original languageEnglish
Article number105
JournalLetters in Mathematical Physics
Issue number4
Early online date2 Aug 2021
Publication statusPublished - Aug 2021


  • Braces
  • Hecke algebras
  • Open quantum spin chains
  • Reflection equation
  • Set-theoretic Yang-Baxter equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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