McKay Correspondence from Quantum Arithmetics Replacing Sum & Product with Direct Sum and Tensor Product?

Abstract

In the TGD framework M₈-H duality relates number theoretic and differential geometric views about physics: Could it provide some understanding of this mystery? The proposal is that for cognitive representations associated with extended Dynkin diagrams (EEDs), Galois group Gal acts as Weyl group on McKay diagrams defined by irreducible representation of the isotropy group Gal_I of given root of a polynomial which is monic polynomial but with roots replaced with direct sums of irreps of Gal_I. This could work for p-adic number fields and finite fields. One also ends up with a more detailed view about the connection between the hierarchies of inclusion of Galois groups associated with functional composites of polynomials and hierarchies of inclusions of hyperfinite factors of type II₁ assignable to the representation of super-symplectic algebra.