Skip to main content
SpringerLink
Log in

Conjugation properties of tensor product and fusion coefficients

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them involving hitherto unnoticed observations on ordinary representation theory of finite simple groups of Lie type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. We use the common convention that the component of the vertex located on the short branch of the Dynkin diagram is written at the end.

References

  1. Coquereaux, R., Zuber, J.-B.: On sums of tensor and fusion multiplicities. J. Phys. A 44, 295208 (2011). arXiv:1103.2943

  2. Coquereaux, R., Zuber, J.-B.: Drinfeld doubles for finite subgroups of SU(2) and SU(3) Lie groups. Sigma 9, 039 (2013). arXiv:1212.4879

  3. Coquereaux, R., Zuber, J.-B.: Conjugation properties of tensor product multiplicities. J. Phys. A 47, 455202 (2014). arXiv:1405.4887

  4. Coquereaux, R., Zuber, J.-B.: On some properties of SU(3) fusion coefficients. Contribution to mathematical foundations of quantum field theory. Special issue Memoriam Raymond Stora. Nucl. Phys. B. doi:10.1016/j.nuclphysb.2016.05.029; arXiv:1605.05864 (2016)

  5. Verlinde, E.: Fusion rules and modular transformations in 2D conformal field theory. Nucl. Phys. B 300, 360–376 (1988)

    Article  ADS  MATH  Google Scholar 

  6. Yau, S.S.-T., Yu, Y.: Gorenstein quotient singularities in dimension three. Mem. Am. Math. Soc. 105(505), 1–88 (1993)

    MathSciNet  MATH  Google Scholar 

  7. Fairbairn, W.M., Fulton, T., Klink, W.H.: Finite and disconnected sugroups of \(SU_3\) and their applications to the elementary-particle spectrum. J. Math. Phys. 5, 1038–1051 (1964)

  8. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997). http://magma.maths.usyd.edu.au

Download references

Author information

Authors and Affiliations

  1. Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France

    Robert Coquereaux

  2. Laboratoire de Physique Théorique et des Hautes Énergies, CNRS UMR 7589, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Jean-Bernard Zuber

Authors
  1. Robert Coquereaux
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Bernard Zuber
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Coquereaux.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Coquereaux, R., Zuber, JB. Conjugation properties of tensor product and fusion coefficients. Lett Math Phys 107, 291–299 (2017). https://doi.org/10.1007/s11005-016-0901-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-016-0901-3

Keywords

Mathematics Subject Classification

Search

Navigation