---
_id: '1452'
abstract:
- lang: eng
  text: 'In this Note we present pairs of hyperkähler orbifolds which satisfy two
    different versions of mirror symmetry. On the one hand, we show that their Hodge
    numbers (or more precisely, stringy E-polynomials) are equal. On the other hand,
    we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which
    in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a
    Calabi-Yau and its mirror should fiber over the same real manifold, with special
    Lagrangian fibers which are tori dual to each other. Our examples arise as moduli
    spaces of local systems on a curve with structure group SL(n); the mirror is the
    corresponding space with structure group PGL(n). The special Lagrangian tori come
    from an algebraically completely integrable Hamiltonian system: the Hitchin system.'
acknowledgement: The authors are grateful for Nigel Hitchin for suggesting the similarity
  between [4] and [12] in 1996 and for Pierre Deligne for numerous useful comments
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
  full_name: Hausel, Tamas
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
- first_name: Michael
  full_name: Thaddeus, Michael
  last_name: Thaddeus
citation:
  ama: 'Hausel T, Thaddeus M. Examples of mirror partners arising from integrable
    systems. <i>Comptes Rendus de l’Academie des Sciences - Series I: Mathematics</i>.
    2001;333(4):313-318. doi:<a href="https://doi.org/10.1016/S0764-4442(01)02057-2">10.1016/S0764-4442(01)02057-2</a>'
  apa: 'Hausel, T., &#38; Thaddeus, M. (2001). Examples of mirror partners arising
    from integrable systems. <i>Comptes Rendus de l’Academie Des Sciences - Series
    I: Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/S0764-4442(01)02057-2">https://doi.org/10.1016/S0764-4442(01)02057-2</a>'
  chicago: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising
    from Integrable Systems.” <i>Comptes Rendus de l’Academie Des Sciences - Series
    I: Mathematics</i>. Elsevier, 2001. <a href="https://doi.org/10.1016/S0764-4442(01)02057-2">https://doi.org/10.1016/S0764-4442(01)02057-2</a>.'
  ieee: 'T. Hausel and M. Thaddeus, “Examples of mirror partners arising from integrable
    systems,” <i>Comptes Rendus de l’Academie des Sciences - Series I: Mathematics</i>,
    vol. 333, no. 4. Elsevier, pp. 313–318, 2001.'
  ista: 'Hausel T, Thaddeus M. 2001. Examples of mirror partners arising from integrable
    systems. Comptes Rendus de l’Academie des Sciences - Series I: Mathematics. 333(4),
    313–318.'
  mla: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising
    from Integrable Systems.” <i>Comptes Rendus de l’Academie Des Sciences - Series
    I: Mathematics</i>, vol. 333, no. 4, Elsevier, 2001, pp. 313–18, doi:<a href="https://doi.org/10.1016/S0764-4442(01)02057-2">10.1016/S0764-4442(01)02057-2</a>.'
  short: 'T. Hausel, M. Thaddeus, Comptes Rendus de l’Academie Des Sciences - Series
    I: Mathematics 333 (2001) 313–318.'
date_created: 2018-12-11T11:52:06Z
date_published: 2001-08-15T00:00:00Z
date_updated: 2023-05-31T09:57:48Z
day: '15'
doi: 10.1016/S0764-4442(01)02057-2
extern: '1'
external_id:
  arxiv:
  - math/0106140
intvolume: '       333'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0106140
month: '08'
oa: 1
oa_version: Preprint
page: 313 - 318
publication: 'Comptes Rendus de l''Academie des Sciences - Series I: Mathematics'
publication_identifier:
  issn:
  - 0764-4442
publication_status: published
publisher: Elsevier
publist_id: '5742'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Examples of mirror partners arising from integrable systems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 333
year: '2001'
...