Tensor product decompositions of representations of Lie algebras
imported>Pythagoras0님의 2013년 12월 12일 (목) 13:41 판
introduction
- various method of tensor product decomposition
- Speiser method
- Bethe ansatz
expositions
- Kumar, Shrawan. 2010. “Tensor Product Decomposition.” In Proceedings of the International Congress of Mathematicians. Volume III, 1226–1261. New Delhi: Hindustan Book Agency. http://www.ams.org/mathscinet-getitem?mr=2827839. http://www.unc.edu/math/Faculty/kumar/papers/kumar60.pdf
- Antoine, Jean-Pierre. 2006. “David Speiser’s Group Theory: From Stiefel’s Crystallographic Approach to Kac-Moody Algebras.” In Two Cultures, edited by Kim Williams, 13–23. Birkhäuser Basel. http://link.springer.com/chapter/10.1007/3-7643-7540-X_2.
- Walton, Mark A. 1990. “Fusion Rules in Wess-Zumino-Witten Models.” Nuclear Physics. B 340 (2-3): 777–790. doi:10.1016/0550-3213(90)90470-X.
- Section 2
- D. Speiser, Theory of Compact Lie Groups and some Applications to Elementary Particle Physics, Group Theoretical Concepts and Methods in Elementary Particle Physics, NATO Summer School Istanbul 1962, pp. 201–276; F. Gürsey, ed. New York: Gordon and Breach, 1964.
articles
- Berenstein, Arkady, and Andrei Zelevinsky. 2001. “Tensor Product Multiplicities, Canonical Bases and Totally Positive Varieties.” Inventiones Mathematicae 143 (1): 77–128. doi:10.1007/s002220000102.
- Grimm, S., and J. Patera. 1997. Decomposition of Tensor Products of the Fundamental Representations of $E_8$. In Advances in Mathematical Sciences: CRM’s 25 Years (Montreal, PQ, 1994), 11:329–355. CRM Proc. Lecture Notes. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1479683.
- Littelmann, Peter. 1995. “Crystal Graphs and Young Tableaux.” Journal of Algebra 175 (1): 65–87. doi:10.1006/jabr.1995.1175.
- Littelmann, Peter. 1994. “A Littlewood-Richardson Rule for Symmetrizable Kac-Moody Algebras.” Inventiones Mathematicae 116 (1-3): 329–346. doi:10.1007/BF01231564.
- Littelmann, Peter. 1990. “A Generalization of the Littlewood-Richardson Rule.” Journal of Algebra 130 (2): 328–368. doi:10.1016/0021-8693(90)90086-4.