Computation Of Global Monodromy For The Hypergeometric Equation

Author: mariam kazaishvili
Keywords: Hypergeometric Equation, Monodromy, Global Monodromy
Annotation:

In this manuscript studies the problem of the connectivity of multi-valued functions for the solution space of hypergeometric equations. The hypergeometric equation, which is given on the extended complex plane, has three regular singular points. Each singular point corresponds to a two-dimensional vector space with its fixed basis, whose elements represent linearly independent solutions in the neighborhood of the singular point. The local monodromy group acts on the solution space, thus obtaining all solutions of the equation. Each locally given solution is extendable along any path that does not pass through a singular point, thus are posed the problem of connecting two solutions, which is expressed in terms of the local monodromy group for the hypergeometric equation solutions. In the manuscript calculates the global monodromy group in terms of hypergeometric functions, using the properties of the fundamental and local monodromy groups of a non-compact Riemann surface. In this way, a new interpretation and novel proof of known results are obtained.

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გლობალური მონოდრომიის გამოთვლა ჰიპერგეომეტრიული განტოლებისთვის [ka]