Irregular hypergeometric D-modules

We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U...

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Detalles Bibliográficos
Autor: Fernández Fernández, María Cruz
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42039
Acceso en línea:http://hdl.handle.net/11441/42039
https://doi.org/10.1016/j.aim.2010.01.017
Access Level:acceso abierto
Palabra clave:Hypergeometric D-module
Gevrey series
Slope
Descripción
Sumario:We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U. Walther in [25] still holds for any full rank integer matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of MA(β) can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case.