SOLUTIONS OF THE tt*-TODA EQUATIONS AND QUANTUM COHOMOLOGY OF MINUSCULE FLAG MANIFOLDS

Yoshiki Kaneko

doi:10.1017/nmj.2022.17

SOLUTIONS OF THE tt*-TODA EQUATIONS AND QUANTUM COHOMOLOGY OF MINUSCULE FLAG MANIFOLDS

Yoshiki Kaneko^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological–antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum field theories. To do this, we combine the Lie-theoretic treatment of the tt*-Toda equations of Guest–Ho with the Lie-theoretic description of the quantum cohomology of minuscule flag manifolds from Chaput–Manivel–Perrin and Golyshev–Manivel.

Original language	English
Pages (from-to)	990-1004
Number of pages	15
Journal	Nagoya Mathematical Journal
Volume	248
DOIs	https://doi.org/10.1017/nmj.2022.17
Publication status	Published - 2022 Dec 10

ASJC Scopus subject areas

Mathematics(all)

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10.1017/nmj.2022.17

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title = "SOLUTIONS OF THE tt*-TODA EQUATIONS AND QUANTUM COHOMOLOGY OF MINUSCULE FLAG MANIFOLDS",

abstract = "We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological–antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum field theories. To do this, we combine the Lie-theoretic treatment of the tt*-Toda equations of Guest–Ho with the Lie-theoretic description of the quantum cohomology of minuscule flag manifolds from Chaput–Manivel–Perrin and Golyshev–Manivel.",

author = "Yoshiki Kaneko",

note = "Funding Information: The author would like to thank Prof. Martin Guest for his considerable support. The author would also like to thank Prof. Takeshi Ikeda and Prof. Takashi Otofuji for their useful discussions and comments. The author would also like to thank the members of geometry group at Waseda for their helpful comments and discussions. Publisher Copyright: {\textcopyright} (2022) The Authors.",

year = "2022",

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doi = "10.1017/nmj.2022.17",

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N1 - Funding Information: The author would like to thank Prof. Martin Guest for his considerable support. The author would also like to thank Prof. Takeshi Ikeda and Prof. Takashi Otofuji for their useful discussions and comments. The author would also like to thank the members of geometry group at Waseda for their helpful comments and discussions. Publisher Copyright: © (2022) The Authors.

PY - 2022/12/10

Y1 - 2022/12/10

N2 - We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological–antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum field theories. To do this, we combine the Lie-theoretic treatment of the tt*-Toda equations of Guest–Ho with the Lie-theoretic description of the quantum cohomology of minuscule flag manifolds from Chaput–Manivel–Perrin and Golyshev–Manivel.

AB - We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological–antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum field theories. To do this, we combine the Lie-theoretic treatment of the tt*-Toda equations of Guest–Ho with the Lie-theoretic description of the quantum cohomology of minuscule flag manifolds from Chaput–Manivel–Perrin and Golyshev–Manivel.

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JF - Nagoya Mathematical Journal

ER -

SOLUTIONS OF THE tt*-TODA EQUATIONS AND QUANTUM COHOMOLOGY OF MINUSCULE FLAG MANIFOLDS

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