# Matrix product solutions to the reflection equation from three dimensional integrability

Abstract : We formulate a quantized reflection equation in which $q$-boson valued $L$ and $K$ matrices satisfy the reflection equation up to conjugation by a solution to the Isaev-Kulish 3D reflection equation. By forming its n-concatenation along the $q$-boson Fock space followed by suitable reductions, we construct families of solutions to the reflection equation in a matrix product form connected to the 3D integrability. They involve the quantum $R$ matrices of the antisymmetric tensor representations of U$_p$ ($A_{n-1}^{(1)}$) and the spin representations of U$_p$($B_n^{(1)}$), $U_p$($D_n^{(1}$) and U$_p$($D_{(n+1)}^{(2)}$)
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Journal articles
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Cited literature [17 references]

https://hal-cea.archives-ouvertes.fr/cea-01748629
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Submitted on : Thursday, March 29, 2018 - 11:43:33 AM
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1802.09164.pdf
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### Citation

Atsuo Kuniba, Vincent Pasquier. Matrix product solutions to the reflection equation from three dimensional integrability. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2018, 51 (25), pp.255204. ⟨10.1088/1751-8121/aac3b4⟩. ⟨cea-01748629⟩

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