Binomial D-modules

• Autores: Dickenstein, Alicia Marcela; Matusevich, Laura Felicia; Miller, Ezra
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Hypergeometric; D-module; Holonomic rank; Horn
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Z d -graded binomial ideal I in C[∂1, . . . , ∂n] along with Euler operators de- fined by the grading and a parameter β ∈ C d . We determine the parameters β for which these D-modules (i) are holonomic (equivalently, regular holonomic, when I is standard-graded); (ii) decompose as direct sums indexed by the primary components of I; and (iii) have holonomic rank greater than the rank for generic β. In each of these three cases, the parameters in question are precisely those outside of a certain explicitly described affine subspace arrangement in C d . In the special case of Horn hypergeometric D-modules, when I is a lattice basis ideal, we furthermore compute the generic holonomic rank combinatorially and write down a basis of solutions in terms of associated A-hypergeometric functions. This study relies fundamentally on the explicit lattice point description of the primary components of an arbitrary binomial ideal in characteristic zero, which we derive in our companion article [DMM08].
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Matusevich, Laura Felicia. Texas A&M University; Estados Unidos
Fil: Miller, Ezra. University Of Minnesota; Estados Unidos