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Guest, Martin A.; Its, Alexander R.; Lin, Chang-Shou

Isomonodromy aspects of the \(tt^*\) equations of Cecotti and Vafa. III: Iwasawa factorization and asymptotics. (English) Zbl 1439.22027

Commun. Math. Phys. 374, No. 2, 923-973 (2020).
Summary: This paper, the third in a series, completes our description of all (radial) solutions on \(\mathbb{C}^*\) of the \(tt^*\)-Toda equations \(2(w_i)_{t\bar{t}} = -e^{2(w_{i+1} - w_i)} + e^{2(w_i - w_{i-1})}\), using a combination of methods from p.d.e., isomonodromic deformations (Riemann-Hilbert method), and loop groups. We place these global solutions into the broader context of solutions which are smooth near 0. For such solutions, we compute explicitly the Stokes data and connection matrix of the associated meromorphic system, in the resonant cases as well as the non-resonant case. This allows us to give a complete picture of the monodromy data, holomorphic data, and asymptotic data of the global solutions.
For part I, II, see [the authors, “Isomonodromy aspects of the \(tt^*\) equations of Cecotti and Vafa I. Stokes data”, arXiv:1209.2045; “Isomonodromy aspects of the \(tt^*\) equations of Cecotti and Vafa II. Riemann-Hilbert problem, arXiv:1312.4825].

Cited in 1 Review
Cited in 7 Documents

MSC:

22E67 Loop groups and related constructions, group-theoretic treatment
22E15 General properties and structure of real Lie groups
22E25 Nilpotent and solvable Lie groups
22E46 Semisimple Lie groups and their representations
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References:

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