Difference between revisions of "Seminar : Quantum affine algebras and spectra of quantum integrable systems"

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* Jimbo, Michio. “Aq-Difference Analogue of U(g) and the Yang-Baxter Equation.” Letters in Mathematical Physics 10, no. 1 (July 1985): 63–69. doi:10.1007/BF00704588.
 
* Jimbo, Michio. “Aq-Difference Analogue of U(g) and the Yang-Baxter Equation.” Letters in Mathematical Physics 10, no. 1 (July 1985): 63–69. doi:10.1007/BF00704588.
 
* Drinfeld, Vladimir G. "Quantum groups." (1986): 789-820. http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0798.0820.ocr.pdf
 
* Drinfeld, Vladimir G. "Quantum groups." (1986): 789-820. http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0798.0820.ocr.pdf
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===finite-dimensional representations of quantum affine algebras===
 
===finite-dimensional representations of quantum affine algebras===

Revision as of 02:46, 12 August 2015

This is the page for the seminar on QFT at the University of Queensland. We focus on Quantum Affine Algebras for Semester 2, 2015. The main goal is to understand various aspects of the theory of quantum affine algebras in mathematical physics.

  • when : Thursdays 3-4:30 pm
  • where : Priestly Building Seminar Room 67-442


topics

Some references are given for each topic. But we won't necessarily follow them strictly or cover them all.

Quantum inverse scattering method (6/8/2015, Jon Links)

  • TQ relations from algebraic Bethe ansatz

introduction (13/8/2015, Chul-hee Lee)

  • overview
  • distribution of the remaining talks

TQ relation of the eight-vertex model (Ole Warnaar)

  • Chapter 10 of [Baxter 1982]
  • Baxter, Rodney J. “Partition Function of the Eight-Vertex Lattice Model.” Annals of Physics 70 (1972): 193–228.

finite-dimensional representations of affine Lie algebras

  • Rao, S. Eswara. “On Representations of Loop Algebras.” Communications in Algebra 21, no. 6 (1993): 2131–53. doi:10.1080/00927879308824668.
  • Senesi, Prasad. “Finite-Dimensional Representation Theory of Loop Algebras: A Survey.” arXiv:0906.0099 [math], May 30, 2009. http://arxiv.org/abs/0906.0099.

quantum affine sl(2) and its finite-dimensional representations

  • Lecture 9 of [EFK 1998]

quantum affine algebras and its realizations

  • Lecture 6 of [EFK 1998]
  • Drinfel'd, V. G. “A New Realization of Yangians and of Quantum Affine Algebras.” Doklady Akademii Nauk SSSR 296, no. 1 (1987): 13–17.
  • Jimbo, Michio. “Aq-Difference Analogue of U(g) and the Yang-Baxter Equation.” Letters in Mathematical Physics 10, no. 1 (July 1985): 63–69. doi:10.1007/BF00704588.
  • Drinfeld, Vladimir G. "Quantum groups." (1986): 789-820. http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0798.0820.ocr.pdf

finite-dimensional representations of quantum affine algebras

  • Chapter 12 of [CP 1995]
  • Chari, Vyjayanthi, and Andrew Pressley. “Quantum Affine Algebras and Their Representations.” In Representations of Groups (Banff, AB, 1994), 16:59–78. CMS Conf. Proc. Amer. Math. Soc., Providence, RI, 1995. http://www.ams.org/mathscinet-getitem?mr=1357195.

theory of q-characters

  • Frenkel, Edward, and Nicolai Reshetikhin. 1999. “The $q$-characters of Representations of Quantum Affine Algebras and Deformations of $\scr W$-algebras.” In Recent Developments in Quantum Affine Algebras and Related Topics (Raleigh, NC, 1998), 248:163–205. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1745260. http://arxiv.org/abs/math/9810055.
  • Knight, Harold. 1995. “Spectra of Tensor Products of Finite-Dimensional Representations of Yangians.” Journal of Algebra 174 (1): 187–196. doi:10.1006/jabr.1995.1123.

TQ relation from representation theoretic point of view

  • Frenkel, Edward, and Nicolai Reshetikhin. 1999. “The $q$-characters of Representations of Quantum Affine Algebras and Deformations of $\scr W$-algebras.” In Recent Developments in Quantum Affine Algebras and Related Topics (Raleigh, NC, 1998), 248:163–205. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1745260. http://arxiv.org/abs/math/9810055.
  • Hernandez, David, and Michio Jimbo. “Asymptotic Representations and Drinfeld Rational Fractions.” Compositio Mathematica 148, no. 5 (2012): 1593–1623. doi:10.1112/S0010437X12000267. http://www.ams.org/mathscinet-getitem?mr=2982441
  • Frenkel, Edward, and David Hernandez. 2013. “Baxter’s Relations and Spectra of Quantum Integrable Models”. ArXiv e-print 1308.3444. http://arxiv.org/abs/1308.3444.

links


references

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</HarvardReferences>

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