TY - JOUR
T1 - Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations
AU - Guest, Martin A.
AU - Ho, Nan Kuo
N1 - Funding Information:
The authors thank Eckhard Meinrenken for useful conversations, and for suggesting the relevance of the Coxeter Plane and the article [ 37 ] by Kostant. They thank Bill Casselman for clarifying the relation between the Coxeter Plane and Coxeter groups ([ 10 ] and “Appendix B”). They also thank Philip Boalch for discussions, and for pointing out the article [ 22 ] by Frenkel and Gross as well as the relevance of twisted connections in the sense of [ 6 ]. 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 Grants 105-2115-M-007-006 and 106-2115-M-007-004.
Funding Information:
The authors thank Eckhard Meinrenken for useful conversations, and for suggesting the relevance of the Coxeter Plane and the article [37] by Kostant. They thank Bill Casselman for clarifying the relation between the Coxeter Plane and Coxeter groups ([10] and ?Appendix B?). They also thank Philip Boalch for discussions, and for pointing out the article [22] by Frenkel and Gross as well as the relevance of twisted connections in the sense of [6]. 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 Grants 105-2115-M-007-006 and 106-2115-M-007-004.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra g, based on the concept of topological–antitopological fusion which was introduced by Cecotti and Vafa. Our main results concern the Stokes data of a certain meromorphic connection, whose isomonodromic deformations are controlled by these equations. First, by exploiting a framework introduced by Boalch, we show that this data has a remarkable structure. It can be described using Kostant’s theory of Cartan subalgebras in apposition and Steinberg’s theory of conjugacy classes of regular elements, and it can be visualized on the Coxeter Plane. Second, we compute canonical Stokes data for a certain family of solutions of the tt*-Toda equations in terms of their asymptotics. To do this, we compute the Stokes data of an auxiliary meromorphic connection, related to the original meromorphic connection by a loop group Iwasawa factorization.
AB - We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra g, based on the concept of topological–antitopological fusion which was introduced by Cecotti and Vafa. Our main results concern the Stokes data of a certain meromorphic connection, whose isomonodromic deformations are controlled by these equations. First, by exploiting a framework introduced by Boalch, we show that this data has a remarkable structure. It can be described using Kostant’s theory of Cartan subalgebras in apposition and Steinberg’s theory of conjugacy classes of regular elements, and it can be visualized on the Coxeter Plane. Second, we compute canonical Stokes data for a certain family of solutions of the tt*-Toda equations in terms of their asymptotics. To do this, we compute the Stokes data of an auxiliary meromorphic connection, related to the original meromorphic connection by a loop group Iwasawa factorization.
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U2 - 10.1007/s00029-019-0494-7
DO - 10.1007/s00029-019-0494-7
M3 - Article
AN - SCOPUS:85069473334
SN - 1022-1824
VL - 25
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 3
M1 - 50
ER -