Maximally reducible monodromy of bivariate hypergeometric systems. (English. Russian original) Zbl 1347.33036
Izv. Math. 80, No. 1, 221-262 (2016); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 1, 235-280 (2016).
The authors compute the monodromy groups of certain families of bivariate systems of partial differential equations of hypergeometric type and investigate their properties. They solve the closely related problem of describing all holomonic bivariate hypergeometric systems in the sense of Horn whose solution space splits into a direct sum of one-dimensional monodromy-invariant subspaces for almost all values of the parameters. Special attention is paid to invariant subspaces of Puiseux polynomial solutions.
Reviewer: Chrysoula G. Kokologiannaki (Patras)
MSC:
33C70 | Other hypergeometric functions and integrals in several variables |
14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
32C38 | Sheaves of differential operators and their modules, \(D\)-modules |
32D15 | Continuation of analytic objects in several complex variables |
32S40 | Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) |
35N10 | Overdetermined systems of PDEs with variable coefficients |
57M05 | Fundamental group, presentations, free differential calculus |