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arXiv · 1801.10445

A Lie-theoretic description of the solution space of the tt*-Toda equations

Martin Guest·Nan-Kuo Ho
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Abstract

We give a Lie-theoretic explanation for the convex polytope which parametrizes the globally smooth solutions of the topological-antitopological fusion equations of Toda type (tt$^*$-Toda equations) which were introduced by Cecotti and Vafa. It is known from [GL] [GIL1] [M1] [M2] that these solutions can be parametrized by monodromy data of a certain flat $SL_{n+1}\mathbb{R}$-connection. Using Boalch's Lie-theoretic description of Stokes data, and Steinberg's description of regular conjugacy classes of a linear algebraic group, we express this monodromy data as a convex subset of a Weyl alcove of $SU_{n+1}$.

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Martin Guest, Nan-Kuo Ho. 2018-01-31. A Lie-theoretic description of the solution space of the tt*-Toda equations. https://doi.org/10.1007/s11040-017-9255-z

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