Brini, A. orcid.org/0000-0002-3758-827X, Ma, J. and Strachan, I.A.B. (Submitted: 2025) Dubrovin duality and mirror symmetry for ADE resolutions. [Preprint - arXiv] (Submitted)
Abstract
We show that, under Dubrovin's notion of ''almost'' duality, the Frobenius manifold structure on the orbit spaces of the extended affine Weyl groups of type ADE is dual, for suitable choices of weight markings, to the equivariant quantum cohomology of the minimal resolution of the du Val singularity of the same Dynkin type. We also provide a uniform Lie-theoretic construction of Landau-Ginzburg mirrors for the quantum cohomology of ADE resolutions. The mirror B-model is described by a one-dimensional LG superpotential associated to the spectral curve of the ADEˆ affine relativistic Toda chain.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Author(s). For reuse permissions, please contact the Author(s). |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Funding Information: | Funder Grant number Engineering and Physical Sciences Research Council EP/S003657/2 Engineering and Physical Sciences Research Council EP/S003657/1 Engineering and Physical Sciences Research Council 2745676 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Feb 2025 17:08 |
Last Modified: | 05 Feb 2025 17:08 |
Status: | Submitted |
Identification Number: | 10.48550/arXiv.2501.05753 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221645 |