ON CLASSIFICATION OF YANGIAN IRREDUCIBLE REPRESENTATIONS OF LIE SUPERALGEBRA SL (1, 2)
Abstract
The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra sl(1,2) – Hopf superalgebra is obtained. The classification is of great use in modern theoretical and mathematical physics. Some feasible applications of this result in mathematical physics are offered.
References
1. Drinfeld V. Quantum groups / V. Drinfeld // Proc. Int. Cong. Math. – V. 1. – Berkley, 1988. – P. 789–820.
2. Dolan L. Yangian Symmetry in D = 4 Superconformal Yang–Mills theory / L. Dolan, Ch. Nappi, E. Witten // arXiv: hep-th/0401243, 2004.
3. Spill F. On Drinfeld’s second realization of the AdS/CFT su(2, 2) Yangian / F. Spill, A. Torrielli // arXiv: hep-th/0803.3194, 2008.
4. Frappat L. Dictionary on Lie Superalgebras / L. Frappat, P. Sorba. – London: Academic Press, 2000.
5. Stukopin V.A. O duble yangiana superalgebry` Li tipa A (m, n) / V.A. Stukopin // Funkcion. analiz i ego prilozhenie. – 2006. – T. 40. – # 2. – C. 81–84. – In Russian.
6. Stukopin V.A. Kvantovy`j dubl` yangiana superalgebry` Li tipa A (m, n) i vy`chislenie universal`noj R-matricy` / V.A. Stukopin // Fundament. i prikladnaya matematika. – 2005. – T. 11. – # 2. – C. 185–208. – In Russian.
7. Stukopin V.A. O yangianax superalgebr Li tipa A (m, n) / V.A. Stukopin // Funkcion. analiz i ego prilozhenie. – 1994. – T. 28. – # 3. – S. 85–88. – In Russian.
8. Kac V. A Sketch of Lie Superalgebra Theory / V. Kac // Commun. Math. Phys. – 1977. – 53. – P. 31–64.
9. Tarasov V.O. O stroenii kvantovy`x L operatorov dlya R-matricy` XXZ modeli / V.O. Tarasov // Teoret. i mat. fizika. – 1984. – T. 61. – # 2. – S. 163–173. – In Russian.
10. Tarasov V.O. Neprivodimy`e matricy` monodromii dlya R-matricy` XXZ modeli i reshyotochny`e kvantovy`e lokal`ny`e gamil`toniany` / V.O. Tarasov // Teoret. i mat. fizika. – 1985. – T. 63. – # 2. – S. 175–196. – In Russian.
11. Zhang R.B. Representations of super Yangian / R.B. Zhang // J. Math. Phys. – 1995. – V. 36. – P. 3854–3865.
Review
For citations:
Stukopin V.A. ON CLASSIFICATION OF YANGIAN IRREDUCIBLE REPRESENTATIONS OF LIE SUPERALGEBRA SL (1, 2). Vestnik of Don State Technical University. 2011;11(8-1):1180-1184. (In Russ.)
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