Binomial D-modules

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Zd-graded binomial ideal I in C[∂1∂n] along with Euler operators defined by the grading and a parameter βεCd 2 Cd. We determine the parameters β for which these D-modules (i) are holonomic (equivalently, r...

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Autor principal: Dickenstein, Alicia Marcela
Publicado: 2010
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein
http://hdl.handle.net/20.500.12110/paper_00127094_v151_n3_p1_Dickenstein
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00127094_v151_n3_p1_Dickenstein
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spelling paper:paper_00127094_v151_n3_p1_Dickenstein2023-06-08T14:35:25Z Binomial D-modules Dickenstein, Alicia Marcela We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Zd-graded binomial ideal I in C[∂1∂n] along with Euler operators defined by the grading and a parameter βεCd 2 Cd. 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 Cd. 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. Fundamental in this study is an explicit lattice point description of the primary components of an arbitrary binomial ideal in characteristic zero, which we derive from a characteristic-free combinatorial result on binomial ideals in affine semigroup rings. Effective methods can be derived for the computation of primary components of arbitrary binomial ideals and series solutions to classical Horn systems. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein http://hdl.handle.net/20.500.12110/paper_00127094_v151_n3_p1_Dickenstein
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Zd-graded binomial ideal I in C[∂1∂n] along with Euler operators defined by the grading and a parameter βεCd 2 Cd. 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 Cd. 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. Fundamental in this study is an explicit lattice point description of the primary components of an arbitrary binomial ideal in characteristic zero, which we derive from a characteristic-free combinatorial result on binomial ideals in affine semigroup rings. Effective methods can be derived for the computation of primary components of arbitrary binomial ideals and series solutions to classical Horn systems.
author Dickenstein, Alicia Marcela
spellingShingle Dickenstein, Alicia Marcela
Binomial D-modules
author_facet Dickenstein, Alicia Marcela
author_sort Dickenstein, Alicia Marcela
title Binomial D-modules
title_short Binomial D-modules
title_full Binomial D-modules
title_fullStr Binomial D-modules
title_full_unstemmed Binomial D-modules
title_sort binomial d-modules
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein
http://hdl.handle.net/20.500.12110/paper_00127094_v151_n3_p1_Dickenstein
work_keys_str_mv AT dickensteinaliciamarcela binomialdmodules
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