Let $K=\Bbb{C}(z)$ with the usual derivation and consider the Airy dierential equation $y^{(2)}-zy$=0. How to determine the monodromy representration? Airy equation is not Fuchsian diferential equation. i am new to monodromy. I have recently started learning monodromy representation of a differential equation from the book 'Algebraic groups and differential galois theory' by Crespo and Hajto. The monodromy representation is in Chapter 7. It will be very helpful someone determines the monodromy representation of the airy equation and describe the steps a little bit so that i can understand it. Can someone explain to me the concept of monodromy representation of a differential equation by analytic continuation of solutions?
2026-03-26 19:18:38.1774552718
Monodromy representation of Airy equation
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The monodromy group of this differential equation is trivial since all coefficients of the equation (they are $1, 0$ and $z$) are analytic functions in a simply-connected domain (the complex plane). See Corollary on Page 92 here. You can find many more details and worked out examples in the linked lecture notes.