Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity

Studying the reduction of type IIB supergravity from ten to three space-time dimensions we describe the metamorphosis of Dynkin diagram for gravity line “caterpillar” into a type IIB supergravity “dragonfly” that is triggered by inclusion of scalars and antisymmetric tensor fields. The final diagram corresponds to type IIB string theory $E_8$ global symmetry group which is the subgroup of the conjectured $E_{11}$ hidden symmetry group. Application of the results for getting the type IIA/IIB T-duality rules and for searching for type IIB vacua solutions is considered.