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

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${}^{\ast }$-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 $S{L}_{n+1}\mathbb{R}$-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 $S{U}_{n+1}$.

27 pages

References in corpus (2)

• Symplectic Manifolds and Isomonodromic Deformations
• Isomonodromy aspects of the tt* equations of Cecotti and Vafa III. Iwasawa factorization and asymptotics

Cited by in corpus (2)

• Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations
• Polytopes, supersymmetry, and integrable systems