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

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Authors

  • Wolfgang Ebeling
  • Sabir M. Gusein-Zade

Research Organisations

External Research Organisations

  • Lomonosov Moscow State University
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Details

Original languageEnglish
Pages (from-to)12305-12329
Number of pages25
JournalInternational Mathematics Research Notices
Volume2021
Issue number16
Publication statusPublished - 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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Cite this

A Version of the Berglund–Hübsch–Henningson Duality With Non-Abelian Groups. / Ebeling, Wolfgang; Gusein-Zade, Sabir M.
In: International Mathematics Research Notices, Vol. 2021, No. 16, 08.2021, p. 12305-12329.

Research output: Contribution to journal › Article › Research › 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 ; Vol. 2021, No. 16. pp. 12305-12329.
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