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Vanishing Cycles and Cartan Eigenvectors

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Abstract

Using the ideas coming from the singularity theory, we study the eigenvectors of the Cartan matrices of finite root systems, and of q-deformations of these matrices

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Notes

  1. This formulation has been suggested by A. Givental.

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Acknowledgements

We are grateful to Misha Finkelberg, Andrei Gabrielov, and Sabir Gusein-Zade for the inspiring correspondence, and to Patrick Dorey for sending us his thesis. Our special gratitude goes to Sasha Givental whose remarks enabled us to generalize some statements and to simplify the exposition and to Maxim Kazarian for the enlightening comments on Gabrielov’s theorem. A.V. thanks MPI in Bonn for hospitality; he was supported in part by NSF Grant DMS-1362924 and the Simons Foundation Grant No. 336826.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062, Toulouse, France

    Laura Brillon & Vadim Schechtman

  2. Laboratoire de Physique Théorique IRSAMC, Université de Toulouse, CNRS,UPS, 31062, Toulouse, France

    Revaz Ramazashvili

  3. Mathematics Department, University of North Carolina, Chapel Hill, NC, USA

    Alexander Varchenko

Authors
  1. Laura Brillon
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  2. Revaz Ramazashvili
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  3. Vadim Schechtman
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  4. Alexander Varchenko
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Corresponding author

Correspondence to Laura Brillon.

Additional information

Revaz Ramazashvili contributed only to writing the Sect. 6.

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Brillon, L., Ramazashvili, R., Schechtman, V. et al. Vanishing Cycles and Cartan Eigenvectors. Arnold Math J. 3, 251–280 (2017). https://doi.org/10.1007/s40598-017-0065-y

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