"Seminar topics on affine Lie algebras"의 두 판 사이의 차이
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==topics== | ==topics== | ||
===Kac-Moody algebras=== | ===Kac-Moody algebras=== | ||
| + | * chapter 1&4 of <ref name="kac" /> | ||
| + | |||
===affine Lie algerbas as central extensions of loop algerbas=== | ===affine Lie algerbas as central extensions of loop algerbas=== | ||
| + | * chapter 7 of <ref name="kac" /> | ||
===Sugawara construction of Virasoro algebra=== | ===Sugawara construction of Virasoro algebra=== | ||
===integrable highest weight representations of affine Lie algebras=== | ===integrable highest weight representations of affine Lie algebras=== | ||
2015년 3월 3일 (화) 18:07 판
This is the webpage for the seminar on Affine Lie Algebras for Semester 1 2015 at the University of Queensland . The goal is to understand various aspects of the theory useful in both mathematics and physics.
Meetings: Thursdays 3-4:30 pm, Priestly Building Seminar Room 67-442
INVITATION EMAIL SENT TO EVERYBODY IN MATH AND PHYSICS
Dear colleagues,
We are having a seminar on Affine Lie Algebras this semester. The goal is to understand various aspects of the theory useful in both mathematics and physics. The seminar will meet once a week on
Thursdays 3:00-4:30 pm - Priestly Building 67-442. The first meeting will be this coming Thursday (March 1).
This is a continuation of the seminar we had last semester regarding mathematical aspects of quantum field theory. Following the approach of the last semester, most of the talks will be given by students and on voluntary basis. The talks will be of informal nature, with lots of questions and discussions. New postgraduate students who are interested in the topic are especially encouraged to participate. We hope to continue to have the presence of the more knowledgable staff to guide us through the intricacies of the subject.
The program of the seminar can be found at: https://sites.google.com/site/masoudkomi/research/qft
This is the only email sent to the mass email list regarding this semester's seminar. If you are not already on the seminar's list and would like to be informed, please send me an email and I will include you in the future announcements.
All the best,
topics
Kac-Moody algebras
- chapter 1&4 of [1]
affine Lie algerbas as central extensions of loop algerbas
- chapter 7 of [1]
Sugawara construction of Virasoro algebra
integrable highest weight representations of affine Lie algebras
Wess-Zumino-Witten model
- Walton, Mark. ‘Affine Kac-Moody Algebras and the Wess-Zumino-Witten Model’. arXiv:hep-th/9911187, 23 November 1999. http://arxiv.org/abs/hep-th/9911187.
modular transformations of characters of affine Lie algebras
- Macdonald, I. G. 1981. “Affine Lie Algebras and Modular Forms.” In Séminaire Bourbaki Vol. 1980/81 Exposés 561–578, 258–276. Lecture Notes in Mathematics 901. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0097202.
fusion rules and Verlinde formula
- Gannon, Terry. 2005. “Modular Data: The Algebraic Combinatorics of Conformal Field Theory.” Journal of Algebraic Combinatorics. An International Journal 22 (2): 211–250. doi:10.1007/s10801-005-2514-2.
- Feingold, Alex J. 2004. ‘Fusion Rules for Affine Kac-Moody Algebras’. In Kac-Moody Lie Algebras and Related Topics, 343:53–96. Contemp. Math. Amer. Math. Soc., Providence, RI. http://www.ams.org/mathscinet-getitem?mr=2056680. http://arxiv.org/abs/math/0212387
- Fuchs, J. 1994. ‘Fusion Rules in Conformal Field Theory’. Fortschritte Der Physik/Progress of Physics 42 (1): 1–48. doi:10.1002/prop.2190420102. http://arxiv.org/abs/hep-th/9306162
- Verlinde, Erik. 1988. “Fusion Rules and Modular Transformations in 2D Conformal Field Theory.” Nuclear Physics B 300: 360–376. doi:10.1016/0550-3213(88)90603-7.
vertex operator constructions of basic representations
- Frenkel, I. B., and V. G. Kac. ‘Basic Representations of Affine Lie Algebras and Dual Resonance Models’. Inventiones Mathematicae 62, no. 1 (81 1980): 23–66. doi:10.1007/BF01391662.
future topics
- admissible representations
- Heisenberg or Virasoro?
memo
links
references
reading for fun
- Berman, Stephen, and Karen Hunger Parshall. ‘Victor Kac and Robert Moody: Their Paths to Kac-Moody Lie Algebras’. The Mathematical Intelligencer 24, no. 1 (13 January 2009): 50–60. doi:10.1007/BF03025312.
- Dolan, Louise. ‘The Beacon of Kac-Moody Symmetry for Physics’. Notices of the American Mathematical Society 42, no. 12 (1995): 1489–95. http://www.ams.org/notices/199512/dolan.pdf
- ↑ 1.0 1.1 1.2 Kac, Victor G. 1994. Infinite-Dimensional Lie Algebras. Cambridge University Press.
- ↑ Francesco, Philippe, Pierre Mathieu, and David Senechal. 1999. Conformal Field Theory. Corrected edition. New York: Springer.
- ↑ Wakimoto, Minoru. Infinite-Dimensional Lie Algebras. Vol. 195. Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 2001. http://www.ams.org/mathscinet-getitem?mr=1793723.
- ↑ Goddard, Peter, and David Olive, eds. Kac-Moody and Virasoro Algebras. Vol. 3. Advanced Series in Mathematical Physics. World Scientific Publishing Co., Singapore, 1988. http://www.ams.org/mathscinet-getitem?mr=966668.