Solitons, Boundaries, and Quantum Affine Algebras

Details Solitons, Boundaries, and Quantum Affine Algebras Solitons, Boundaries, and Quantum Affine Algebras

2002-12-23

arxiv.org/abs/math/0212317v2

Mathematics

Quantum Algebra

Talk delivered at the Ramanujan International Symposium on Kac-Moody Lie algebras and Applications in Chennai in January 2002,

Scientific paper

This is a condensed write-up of a talk delivered at the Ramanujan International Symposium on Kac-Moody Lie algebras and Applications in Chennai in January 2002. The talk introduces special coideal subalgebras of quantum affine algebras which appear in physics when solitons are restricted to live on a half-line by an integrable boundary condition. We review how the quantum affine symmetry determines the soliton S-matrix in affine Toda field theory and then go on to use the unbroken coideal subalgebra on the half-line to determine the soliton reflection matrix. This gives a representation theoretic method for the solution of the reflection equation (boundary Yang-Baxter equation) by reducing it to a linear equation.

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