Rational K-matrices and representations of twisted Yangians

Abstract

We describe the twisted Yangians Y(g,h) which arise as boundary remnants of Yangians Y(g) in 1+1D integrable field theories. We describe and extend our recent construction of the intertwiners of their representations (the rational boundary S- or 'K'-matrices) and perform a case-by-case analysis for all pairs (g,h), giving the h-decomposition of Y(g,h)-representations where possible.

16 pages. v3 has minor corrections and updates, and more detail on Casimir normalizations

References in corpus (4)

• Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
• Representations of reflection algebras
• R-matrices and Tensor Product Graph Method
• Magic squares and matrix models of Lie algebras

Cited by in corpus (26)

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• The generalized non-linear Schrodinger model on the interval
• Twisted Yangians for symmetric pairs of types B, C, D
• On reflection algebras and twisted Yangians
• Classically integrable boundary conditions for symmetric-space sigma models
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Quantum integrability of sigma models on AII and CII symmetric spaces
• Gauge Theory and Boundary Integrability
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers
• Drinfeld J Presentation of Twisted Yangians
• Reflection algebras for sl(2) and gl(1|1)
• On the classification of rational K-matrices
• From Twisted Quantum Loop Algebras to Twisted Yangians
• Affine $ı$quantum groups and twisted Yangians in Drinfeld presentations
• Thermodynamic Bethe ansatz for the AII sigma-models
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• Solitons, Boundaries, and Quantum Affine Algebras
• A Drinfeld type presentation of twisted Yangians
• Bulk and boundary $g_2$ factorized S-matrices
• Twisted Yangian symmetry of the open Hubbard model
• Twisted super Yangians of type AIII and their representations
• Twisted Yangians and symmetric pairs