# The reflection equation: history, concepts and solutions

**Date**: Friday 14 December 2018, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Seminars, Applied Mathematics, Integrable Systems**Cost**: free

#### Bart Vlaar, Heriot-Watt University

Quantum integrability is typically underpinned by factorizability criteria (say, of a scattering process). Away from boundaries this is the Yang-Baxter equation, a cubic relation which is intimately connected to particular Hopf algebras known as affine quantum groups and their representations. In the presence of a boundary, a quartic relation known as the reflection equation is the natural analogue. It arises naturally in the representation theory of certain pairs (affine quantum group, coideal subalgebra).

We will survey this and highlight some recent work, namely the classification of all solutions in the case of quantum affine sl_N and its lowest-dimensional representation

This is joint with V. Regelskis.