A Version of the Berglund–Hübsch–Henningson Duality With Non-Abelian Groups

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Organisationseinheiten

Externe Organisationen

  • Lomonosov Moscow State University
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Details

OriginalspracheEnglisch
Seiten (von - bis)12305-12329
Seitenumfang25
FachzeitschriftInternational Mathematics Research Notices
Jahrgang2021
Ausgabenummer16
PublikationsstatusVeröffentlicht - Aug. 2021

Abstract

A. Takahashi suggested a conjectural method to find mirror symmetric pairs consisting of invertible polynomials and symmetry groups generated by some diagonal symmetries and some permutations of variables. Here we generalize the Saito duality between Burnside rings to a case of non-abelian groups and prove a "non-abelian" generalization of the statement about the equivariant Saito duality property for invertible polynomials. It turns out that the statement holds only under a special condition on the action of the subgroup of the permutation group called here PC ("parity condition"). An inspection of data on Calabi-Yau threefolds obtained from quotients by non-abelian groups shows that the pairs found on the basis of the method of Takahashi have symmetric pairs of Hodge numbers if and only if they satisfy PC.

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A Version of the Berglund–Hübsch–Henningson Duality With Non-Abelian Groups. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
in: International Mathematics Research Notices, Jahrgang 2021, Nr. 16, 08.2021, S. 12305-12329.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ebeling W, Gusein-Zade SM. A Version of the Berglund–Hübsch–Henningson Duality With Non-Abelian Groups. International Mathematics Research Notices. 2021 Aug;2021(16):12305-12329. doi: 10.48550/arXiv.1807.04097, 10.1093/imrn/rnz167
Ebeling, Wolfgang ; Gusein-Zade, Sabir M. / A Version of the Berglund–Hübsch–Henningson Duality With Non-Abelian Groups. in: International Mathematics Research Notices. 2021 ; Jahrgang 2021, Nr. 16. S. 12305-12329.
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