A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations

Martin A. Guest; Nan Kuo Ho

doi:10.1007/s11040-017-9255-z

A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations

Martin A. Guest, Nan Kuo Ho

基幹理工学部

研究成果: Article › 査読

2 被引用数 (Scopus)

抄録

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 Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) that these solutions can be parametrized by monodromy data of a certain flat SL_{n+ 1}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}.

本文言語	English
論文番号	24
ジャーナル	Mathematical Physics Analysis and Geometry
巻	20
号	4
DOI	https://doi.org/10.1007/s11040-017-9255-z
出版ステータス	Published - 2017 12 1

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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10.1007/s11040-017-9255-z

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引用スタイル

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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 Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) that these solutions can be parametrized by monodromy data of a certain flat SLn+ 1ℝ-connection. Using Boalch{\textquoteright}s Lie-theoretic description of Stokes data, and Steinberg{\textquoteright}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.",

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author = "Guest, {Martin A.} and Ho, {Nan Kuo}",

note = "Funding Information: Acknowledgements The authors thank Philip Boalch, Ralf Kurbel, and Eckhard Meinrenken for useful conversations. The first author was partially supported by JSPS grant (A) 25247005. He is grateful to the National Center for Theoretical Sciences for excellent working conditions and financial support. The second author was partially supported by MOST grant 104-2115-M-007-004. She is grateful to the Japan Society for the Promotion of Science for the award of a Short-Term Invitation Fellowship.",

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N2 - 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 Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) 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.

AB - 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 Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) 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.

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