arXiv subjects
Publications and source records attributed to Abdellah Sebbar.
For any discrete group $Γ$ and any 2-dimensional complex representation $ρ$ of $Γ$, we introduce the notion of $ρ-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also provide examples arising from the monodromy of differential equations.
The purpose of this paper is to solve various differential equations having Eisenstein series as coefficients using various tools and techniques. The solutions are given in terms of modular forms, modular functions and equivariant forms.
Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the ADE geometries involved in building Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and the holomorphic wave equations representing these non-commutative geometries. The spectrum of the holomorphic waves is interpreted as the quantum moduli space. Quantum A_1 geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.