Abstract
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the Gerdjikov-Ivanov (GI) hierarchy. Our main tools include the polynomial recursive formalism, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the Baker-Akhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire GI hierarchy.
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