Reflection algebras for sl(2) and gl(1|1)
arXiv:1206.6498
Abstract
We present a generalization the G. Letzter's theory of quantum symmetric pairs of semisimple Lie algebras for the case of quantum affine algebras. We then study solutions of the reflection equation for the quantum affine algebras sl(2) and gl(1|1) and their Yangian limit for singlet (diagonal) and vector (non-diagonal) boundary conditions. We construct the corresponding quantum affine coideal subalgebras that are based on the quantum symmetric pairs, and the (generalized) twisted Yangians.
31 page; v2: updated version
References in corpus (9)
- Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
- Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
- Rational K-matrices and representations of twisted Yangians
- Coideal algebras from twisted Manin triples
- Generalized q-Onsager algebras and boundary affine Toda field theories
- On boundary super algebras
- New reflection matrices for the U_q(gl(m|n)) case
- Twisted superYangians and their representations
- Reflection equation algebras, coideal subalgebras, and their centres