99
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Theta Functions for Lattices of SU(3) Hyper-Roots

References

  • [Cappelli et al. 87] A. Cappelli, C. Itzykson, and J. -B. Zuber, “The ADE Classification of Minimal and A(1)1 Conformal Invariant Theories.” Commun. Math. Phys. 13 (1987), 1–26.
  • [Conway and Sloane 99] J. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, third edition. New York: Springer, 1999.
  • [Coquereaux 14] R. Coquereaux, “Quantum McKay Correspondence and Global Dimensions for Fusion and Module-Categories Associated with Lie Groups.” J. Algebra 398 (2014), 258–283.
  • [Coquereaux XX] R. Coquereaux, “Fusion Graphs.” Available online (http://www.cpt.univ-mrs.fr/coque/quantumfusion/FusionGraphs.html), 2009.
  • [Coquereaux et al. 06] R. Coquereaux, D. Hammaoui, G. Schieber, and E. H. Tahri, “Comments About Quantum Symmetries of SU(3) Graphs.” J. Geom. Phys. 57 (2006), 269–292.
  • [Coquereaux and Schieber 07] R. Coquereaux and G. Schieber, “Orders and Dimensions for sl2 or sl3 Module-Categories and Boundary Conformal Field Theories on a Torus.” J. Math. Phys. 48 (2007), 043511. Available online (http://arxiv.org/abs/math-ph/0610073).
  • [Coquereaux and Zuber 16] R. Coquereaux and J.-B. Zuber, “On Some Properties of SU(3) Fusion Coefficients.” Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora. Nucl. Phys. B., 912C (2016), 119–150. DOI: 10.1016/j.nuclphysb.2016.05.029.
  • [Deza and Grishukhin 95] M. Deza and V. Grishukhin, “Delaunay Polytopes of Cut Lattices.” Linear Algebra Appl. 226–228 (1995), 667–685.
  • [Di Francesco et al. 97] P. Di Francesco, P. Matthieu, and D. Senechal, Conformal Field Theory. New York: Springer, 1997.
  • [Di Francesco and Zuber 90] P. Di Francesco, and J.-B. Zuber, “SU(N) Lattice Integrable Models Associated with Graphs,” Nucl. Phys. B 338 (1990), 602–646.
  • [Dorey 93] P. Dorey, “Partition Functions, Intertwiners and the Coxeter Element.’ Int. J. Mod. Phys A8 (1993), 193–208. arXiv:hep-th/9205040.
  • [Evans and Pugh 09] D. E. Evans and M. Pugh, “Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs.” Münster J. Math. 2 (2009), 95–142.
  • [Finkelberg 96] M. Finkelberg, “An Equivalence of Fusion Categories.” Geom. Funct. Anal. 6 (1996), 249–267.
  • [Huang 05] Y.-Z. Huang, “Vertex Operator Algebras, the Verlinde Conjecture, and Modular Tensor Categories.” Proc. Natl. Acad. Sci. USA 102 (2005), 5352–5356.
  • [Kac 90] V. Kac, Infinite Dimensional Lie Algebras. Cambridge: Cambridge University Press, 1990.
  • [Kazhdan and Lusztig 94] D. Kazhdan and G. Lusztig, “Tensor Structures Arising from Affine Lie Algebras, III.” J. Amer. Math. Soc. 7 (1994), 335–381.
  • [Kirillov and Ostrik 02] A. Kirillov and V. Ostrik, “On q-Analog of McKay Correspondence and ADE Classification of SL2 Conformal Field Theories.” Adv. Math. 171-2 (2002), 183–227.
  • [Ocneanu 99] A. Ocneanu, “Paths on Coxeter Diagrams: From Platonic Solids and Singularities to Minimal Models and Subfactors, Notes by Goto S.” in Lectures on Operator Theory, Fields Institute Monographs, edited by R. Bhat, et al., pp. 243–323. Providence, RI: AMS Publications, 1999.
  • [Ocneanu 00a] A. Ocneanu, “The Classification of Subgroups of Quantum SU(N).” in, Quantum Symmetries in Theoretical Physics and Mathematics, Bariloche 2000, vol. 294, edited by R. Coquereaux, A. García, and R. Trinchero, pp. 133–160. Providence, RI: AMS Contemporary Mathematics., 2000.
  • [Ocneanu 00b] A. Ocneanu, “Higher Coxeter systems.” Available online (http://www.msri.org/publications/ln/msri/2000/subfactors/ocneanu), 2000.
  • [Ocneanu XXa] A. Ocneanu, Poster communications, Penn State Department of Mathematics, State College, PA.
  • [Ocneanu XXb] A. Ocneanu, Book to appear (work in progress).
  • [Ostrik 03] V. Ostrik, “Module Categories, Weak Hopf Algebras and Modular Invariants.” Transform. Groups 8: 2 (2003), 177–206.
  • [Plesken and Pohst XX] W. Plesken and M. Pohst, “Constructing Integral Lattices with Prescribed Minimum.” Math. Comput. 45: 171 (1985), 209–221, and supplement S5–S16.
  • [Wieb et al. 97] B. Wieb, C. John, and P. Catherine, “The Magma Algebra System. I. The User Language.” J. Symb. Comput. 24 (1997), 235–265. Available online (http://magma.maths.usyd.edu.au).
  • [Wolfram Research 10] Wolfram Research, Inc. Mathematica. Champaign, IL: Wolfram Research, Inc., 2010.
  • [Zagier 08] D. B. Zagier, “Elliptic Modular Forms and Their Applications.” in The 1-2-3 of Modular Forms: Lectures at a Summer School in Nordfjordeid, Norway, (2004), pp. 1–103, edited by K. Ranestad. New York: Springer, 2008.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.