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 SLn+1R-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 SUn+1.
MSC Codes 81T40, 22E10, 53C43, 34M40
|Publication status||Published - 2018 Jan 31|
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