Jordan-Schwinger Representations and Factorised Yang-Baxter Operators

The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of Jordan-Schwinger representations. The latter are formulated explicitly. On this basis the parameter exchange and intertwining operators are derived.Comment: based on a contribution to ISQS200

Yangian symmetric correlators, R operators and amplitudes

Yangian symmetric correlators can be constructed by the action of Yang-Baxter R operators on trivial basic correlators. The example of a four-point correlator is given in two representations and the construction of the completely connected N point correlator is described. The helicity representation is dicussed and the relation of the four-point correlator to tree-level scattering amplitudes is shown

Integrable chains with Jordan - Schwinger representations

The restiction to the class of Jordan - Schwinger representations of s`(n+1) results in simple relations for the L matrices and in explicit expressions for the general Yang-Baxter operators as products of two parameter permutation operators. Limits are studied which are related to the finite dimensional representations and to degenerate Yangians. The analogy to the s`(2) case leads to analogous forms of global spin chain operators

Orthogonal and symplectic Yangians

We consider Yang-Baxter relations with orthogonal or symplectic symmetry, in particular L matrices defining the related Yangian algebra. We study the conditions resulting from the truncation of the expansion of L(u)

QCD at High Energies and Yangian Symmetry

Yangian symmetric correlators provide a tool to investigate integrability features of QCD at high energies. We discuss the kernel of the equation of perturbative Regge asymptotics, the kernels of the evolution equation of parton distributions, Born scattering amplitudes and coupling renormalization

Orthogonal and symplectic Yangians: oscillator realization

We solve RLL-relation with fundamental orthogonal/symplectic R-matrix examining polynomial with respect to u expressions for L-operator. We use creation-annihilation operators to construct a realization of Yangian generators

Monodromy operators and symmetric correlators

Yangian symmetric correlators are defined as eigenfunctions of monodromy operators. Examples and relations are given and an evaluation method of the symmetry condition is described

Parton Distribution Functions and Tensorgluons

We derive the regularised evolution equations for the parton distribution functions that include tensorgluons

The Roles of APC and Axin Derived from Experimental and Theoretical Analysis of the Wnt Pathway

Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator β-catenin. Recent studies have demonstrated that axin, which coordinates β-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3β, APC, axin, β-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein–protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on β-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of β-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity