Restriction of hypergeometric 𝒟-modules with respect to coordinate subspaces

Fernández-Fernández, María-Cruz; Walther, Uli

doi:10.1090/S0002-9939-2011-10836-0

Restriction of hypergeometric $\mathscr {D}$-modules with respect to coordinate subspaces
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by María-Cruz Fernández-Fernández and Uli Walther PDF

Proc. Amer. Math. Soc. 139 (2011), 3175-3180 Request permission

Abstract:

We compute the restriction of an $A$-hypergeometric $\mathscr {D}$-module with respect to a coordinate subspace under certain genericity conditions on the parameter.

References

Francisco Jesús Castro-Jiménez and Nobuki Takayama, Singularities of the hypergeometric system associated with a monomial curve, Trans. Amer. Math. Soc. 355 (2003), no. 9, 3761–3775. MR 1990172, DOI 10.1090/S0002-9947-03-03300-2
María-Cruz Fernández-Fernández and Francisco Jesús Castro-Jiménez, Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve, Trans. Amer. Math. Soc. 363 (2011), no. 2, 923–948.
I. M. Gel′fand, M. I. Graev, and A. V. Zelevinskiĭ, Holonomic systems of equations and series of hypergeometric type, Dokl. Akad. Nauk SSSR 295 (1987), no. 1, 14–19 (Russian); English transl., Soviet Math. Dokl. 36 (1988), no. 1, 5–10. MR 902936
I. M. Gel′fand, A. V. Zelevinskiĭ, and M. M. Kapranov, Hypergeometric functions and toric varieties, Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 12–26 (Russian); English transl., Funct. Anal. Appl. 23 (1989), no. 2, 94–106. MR 1011353, DOI 10.1007/BF01078777
Yves Laurent and Zoghman Mebkhout, Image inverse d’un $\scr D$-module et polygone de Newton, Compositio Math. 131 (2002), no. 1, 97–119 (French, with English summary). MR 1895922, DOI 10.1023/A:1014761415793
Laura Felicia Matusevich, Ezra Miller, and Uli Walther, Homological methods for hypergeometric families, J. Amer. Math. Soc. 18 (2005), no. 4, 919–941. MR 2163866, DOI 10.1090/S0894-0347-05-00488-1
Philippe Maisonobe and Tristan Torrelli, Image inverse en théorie des $\scr D$-modules, Éléments de la théorie des systèmes différentiels géométriques, Sémin. Congr., vol. 8, Soc. Math. France, Paris, 2004, pp. 1–57 (French, with English and French summaries). MR 2077644
Toshinori Oaku, Algorithms for $b$-functions, restrictions, and algebraic local cohomology groups of $D$-modules, Adv. in Appl. Math. 19 (1997), no. 1, 61–105. MR 1453406, DOI 10.1006/aama.1997.0527
Toshinori Oaku and Nobuki Takayama, Algorithms for $D$-modules—restriction, tensor product, localization, and local cohomology groups, J. Pure Appl. Algebra 156 (2001), no. 2-3, 267–308. MR 1808827, DOI 10.1016/S0022-4049(00)00004-9
Mutsumi Saito, Isomorphism classes of $A$-hypergeometric systems, Compositio Math. 128 (2001), no. 3, 323–338. MR 1858340, DOI 10.1023/A:1011877515447
Bernd Sturmfels and Nobuki Takayama, Gröbner bases and hypergeometric functions, Gröbner bases and applications (Linz, 1998) London Math. Soc. Lecture Note Ser., vol. 251, Cambridge Univ. Press, Cambridge, 1998, pp. 246–258. MR 1708882
Mathias Schulze and Uli Walther, Hypergeometric D-modules and twisted Gauß-Manin systems, J. Algebra 322 (2009), no. 9, 3392–3409. MR 2567427, DOI 10.1016/j.jalgebra.2008.09.010
Uli Walther, Duality and monodromy reducibility of $A$-hypergeometric systems, Math. Ann. 338 (2007), no. 1, 55–74. MR 2295504, DOI 10.1007/s00208-006-0067-x