The fundamental representation of \newcommand{\alg}[1]{\mathfrak{#1}} \alg{su}(N):This representation of the Yangian plays a role in various different contexts, e.g. for the Heisenberg spin chain or the chiral Gross-Neveu model. Moreover, this case serves as a warm-up exercise for the more involved dynamical representations of AdS/CFT and to introduce our methodology

The fundamental representation of \newcommand{\alg}[1]{\mathfrak{#1}} \alg{u}(1|1) (undynamic and dynamic):Adding supersymmetry to the above problem, we consider the dynamic representations of [, 31: #aaae7ffbib031] which are relevant to the scattering in the \newcommand{\alg}[1]{\mathfrak{#1}} \alg{su}(2|1) sector of \newcommand{\superN}{\mathcal{N}} \superN=4 SYM theory. While the dynamic property of a rapidity-dependent action of the symmetry generators is implemented, some of the complications of the full AdS/CFT scattering problem (e.g. braiding factors) are still projected out in this case. We also discuss the Yangian constraints in the undynamic limit which represents the scattering in conventional spin chain models

The fundamental representation of \newcommand{\alg}[1]{\mathfrak{#1}} \alg{su}(2|2)(\ltimes \mathbb{R}^2) (undynamic and dynamic):Finally, we consider the full symmetry algebra underlying the scattering in AdS/CFT. The new feature of its dynamic representation is given by non-trivial braiding factors that render the action of the Lie algebra generators (the level 0 of the Yangian) nonlocal. Again we consider the full dynamic representation, as well as its undynamic limit that plays a role in the condensed matter literature

Yangians, S-matrices and AdS/CFT J. Phys. A: Math. Theor. 44 263001

Lectures on Yangian symmetry J. Phys. A: Math. Theor. 49 323002

Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory Strangeness in Quark Matter. Proc. Int. Conf. Beijing, P.R

Exact S