Kirillov-Reshetikhin modules and fusion rings from CFT

remarks

• a brief exposition is given at On the boundary of Q-systems : introduction to the KNS conjecture

talks

• Seminar on Algebra, Geometry and Physics, MPI, 9/July/2013

references

origin of the problem

• Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:10.1142/S0217751X89000042.
• A. N. Kirillov (1989), Identities for the Rogers Dilogarithm Function Connected with Simple Lie Algebras. Journal of Soviet Mathematics 47
• Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:10.1088/0305-4470/23/9/012.: 2450–2459. doi:10.1007/BF01840426.
• Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity. Nuclear Physics B, 389(1), 209–244. doi:10.1016/0550-3213(93)90291-V

review paper

• Kuniba, A., Nakanishi, T., & Suzuki, J. (2011). T -systems and Y -systems in integrable systems. Journal of Physics A: Mathematical and Theoretical, 44(10), 103001. High Energy Physics - Theory; Mathematical Physics; Mathematical Physics; Quantum Algebra; Exactly Solvable and Integrable Systems. doi:10.1088/1751-8113/44/10/103001
  • see chapters 13 and 14

my papers

• A proof of the KNS conjecture : $D_r$ case, J. Phys. A: Math. Theor. 46 165201 doi:10.1088/1751-8113/46/16/165201, arXiv:1210.1669
• Positivity and Periodicity of $Q$-systems in the WZW fusion ring arxiv:1302.1467

pdf

• File:Kirillov-Reshetikhin modules and fusion rings from CFT.pdf