We introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution.
A quantized Riemann-Hilbert problem in Donaldson-Thomas theory / A. Barbieri, T. Bridgeland, J. Stoppa. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2022:5(2022 Mar), pp. 3417-3456. [10.1093/imrn/rnaa294]
A quantized Riemann-Hilbert problem in Donaldson-Thomas theory
A. BarbieriPrimo
;
2022
Abstract
We introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution.
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