Functorial Localization Formula on Mirror Principles

This paper focuses on function theory or representation theories in a very elegant and substantial way in geometry. It is very interesting to see how special functions enter into geometry. We like to point out that Symmetric, Trigonometric and Theta- functions are representation theoretic formula, equivariant Euler classes, and the geometry of moduli spaces of stable maps. The boundary of these holomorphic discs lie in certain special Lagrangian sub-manifold, which have boundary in some vanishing cycle.Keywords : Mirror principles, Symmetric series, linear sigma model, Euler data, hypergeometric series