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| Witten's $D_4$ Integrable Hierarchies Conjecture |
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Citation： |
Huijun FAN,Amanda FRANCIS,Tyler JARVIS,Evan MERRELL,Yongbin RUAN.Witten's $D_4$ Integrable Hierarchies Conjecture[J].Chinese Annals of Mathematics B,2016,37(2):175~192 |
| Page view： 7161
Net amount： 4344 |
Authors： |
Huijun FAN; Amanda FRANCIS;Tyler JARVIS;Evan MERRELL;Yongbin RUAN |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11325101, 11271028), the
National Security Agency of USA (No.H98230-10-1-0181) and the Doctoral Fund of the Ministry of Education of China (No.20120001110060). |
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| Abstract： |
The authors prove that the total descendant potential functions of
the theory of Fan-Jarvis-Ruan-Witten for $D_4$ with symmetry group
$\genj$ and for $D_4^T$ with symmetry group $G_{\rm max}$,
respectively, are both tau-functions of the $D_4$
Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof,
begun in the article by Fan-Jarvis-Ruan (2013), of the Witten
Integrable Hierarchies Conjecture for all simple (ADE)
singularities. |
Keywords： |
Quantum cohomology, Frobenius manifolds, Singularity theory,\newline Integrable hierarchies
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Classification： |
14N35, 53D45, 32S05, 37K10, 37K20, 35Q53 |
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