Seminar : Quantum affine algebras and spectra of quantum integrable systems

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.

TQ relations from algebraic Bethe ansatz (6/8/2015, Jon Links)

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

overview
distribution of the remaining talks

TQ relation in eight-vertex model (Ole Warnaar)

Chapter 10 of [Baxter 1982]

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

Lecture 9 of [EFK 1998]

quantum affine algebras or Drinfeld-Jimbo quantum groups (quantized UEA)

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.

finite-dimensional representations of affine Lie algebras

Senesi, Prasad. “Finite-Dimensional Representation Theory of Loop Algebras: A Survey.” arXiv:0906.0099 [math], May 30, 2009. http://arxiv.org/abs/0906.0099.

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.
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

[*EFK 1998] Etingof, Pavel I., Igor B. Frenkel, and Alexander A. Kirillov Jr. Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations. Vol. 58. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1998. http://www.ams.org/mathscinet-getitem?mr=1629472.
[*CP 1995] Chari, Vyjayanthi, and Andrew Pressley. A Guide to Quantum Groups. Cambridge University Press, Cambridge, 1995. http://www.ams.org/mathscinet-getitem?mr=1358358.
[*Baxter 1982] R. J. Baxter, "Exactly Solved Models in Statistical Mechanics" Academic Press, 1982 http://www.ams.org/mathscinet-getitem?mr=998375. http://physics.anu.edu.au/theophys/baxter_book.php

</HarvardReferences>

Drinfeld, Vladimir G. "Quantum groups." (1986): 789-820. http://www.mathunion.org/ICM/ICM1986.1/Main/icm1986.1.0798.0820.ocr.pdf