About the generalization of dual conformal symmetry and Yangian in TGD
The discovery of dual of the conformal symmetry of gauge theories was crucial for the development of twistor Grassmannian approach. The D=4 conformal generators acting on twistors have a dual representation in which they act on momentum twistors: one has dual conformal symmetry, which becomes manifest in this representation. These two separate symmetries extend to Yangian symmetry providing a powerful constraint on the scattering amplitudes in twistor Grassmannian approach fo N=4 SUSY.
In TGD the conformal Yangian extends to super-symplectic Yangian - actually, all symmetry algebras have a Yangian generalization with multi-locality generalized to multi-locality with respect to partonic 2-surfaces. The generalization of the dual conformal symmetry has however remained obscure. In the following I describe what the generalization of the two conformal symmetries and Yangian symmetry would mean in TGD framework.
One also ends up with a proposal of an information theoretic duality between Euclidian and Minkowskian regions of the space-time surface inspired by number theory: one might say that the dynamics of Euclidian regions is mirror image of the dynamics of Minkowskian regions. A generalization of the conformal reflection on sphere and of the method of image charges in 2-D electrostatics to the level of space-time surfaces allowing a concrete construction reciple for both Euclidian and Minkowskian regions of preferred extremals is in question. One might say that Minkowskian and Euclidian regions are analogous to Leibnizian monads reflecting each other in their internal dynamics.
For a summary of earlier postings see Latest progress in TGD.