Hessian polyhedra, invariant theory and Appell hypergeometric functions - Yang, Lei (Mathematics professor) (World Scientific Publishing Company Pte Limited, 2018)
"Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group 𝔊′216. It provides another beautiful example on the fundamental unity of mathematics."--
Includes bibliographical references
Geometry and arithmetic associated with Appell hypergeometric functions -- Hessian polyhedra, invariant theory and Appell hypergeometric functions -- Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated hessian polyhedra
Keywords: Affine algebraic groups; Group schemes (Mathematics); Transformations (Mathematics); Polyhedra; Hypergeometric functions; Electronic books