Gombor Tamas (Wigner RMI): On classification of rational K-matrices

Friday 17 May 2019, 14:00 → 16:00 Europe/Budapest

Tanacsterem

The K-matrices are solutions of the boundary Yang-Baxter equation. Their main application area is open spin chains and they also describe boundary scatterings of 1+1 dimensional integrable field theories. Based on the simplest known K-matrices, it was conjectured that the boundary breaks the bulk symmetry G to H such that G/H is a symmetric space, which means that there exists a Lie-group involution for which the subgroup H is invariant. 

Some K-matrices belong to representation of the so called twisted Yangians which are coidal subalgebras of Yangians. There are one-to-one correspondence between twisted Yangians and symmetric spaces which also shows the connection between the solutions of the boundary Yang-Baxter equation and symmetric spaces. In this talk I prove that if a K-matrix is a solution of the boundary Yang-Baxter equation then the residual symmetry always defines a symmetric space.