Quantum Reduction for AFfine Superalgebras

Communications in Mathematical Physics

Volumn 241, Issue 2-3, 2003, Pages 307-342

  Kac, Victor ^a   Roan, Shi Shyr ^b   Wakimoto, Minoru ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b INSTITUTE OF MATHEMATICS   (Taiwan)

^c KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242275987     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0926-1     Document Type: Article

References (29)

1. [BK] Bakalov, B., Kac, V. G.: Field algebras. IMRN 3, 123-159 (2003) QA/ 0204282
2. [B] Bershadsky, M.: Conformal field theory via Hamiltonian reduction. Commun. Math. Phys. 139, 71-82(1991)
3. [BeK] Bershadsky, M.: Phys. Lett. 174B, 285 (1986); V.G. Knizhnik, Theor. Math. Phys. 66, 68 (1986)
4. [BeK] Bershadsky, M.: Phys. Lett. 174B, 285 (1986); V.G. Knizhnik, Theor. Math. Phys. 66, 68 (1986)
5. [BT] de Boer, J., Tjin, T.: The relation between quantum W-algebras and Lie algebras. Commun. Math. Phys. 160, 317-332 (1994).
6. [BS] Bouwknegt, P., Schoutens, K.: W-symmetry. Advanced ser Math. Phys., Vol 22, Singapore: World Scientific, 1995
7. [D] Dobrev, V. K.: Characters of the unitarizable highest weight modules over N = 2 superconformal algebras. Phys. Lett. B 186, 43-51 (1987)
8. [FF1] Feigin, B.L., Frenkel, E.: Quantization of Drinfeld-Sokolov reduction. Phys. Lett. B 246, 75-81 (1990)
9. [FF2] Feigin, B.L., Frenkel, E.: Representations of affine Kac-Moody algebras, bozonization and resolutions. Lett. Math. Phys. 19, 307-317 (1990)
10. [F] Fiebig, P.: The combinatorics of category script O sign for symmetrizable Kac-Moody algebras. 2002 preprint
11. [FL] Fradkin, E.S., Linetsky, V. Ya.: Classification of superconformal and quasisuperconformal algebras in two dimensions. Phys. Lett. B 291, 71-76 (1992)
12. [FKW] Frenkel, E., Kac, V., Wakimoto, M.: Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction. Commun. Math. Phys. 147, 295-328 (1992)
13. [GS] Goddard, P., Schwimmer, A.: Factoring out free fermions and superconformal algebras. Phys. Lett. 214B, 209-214 (1988)
14. [K1] Kac, V.G.: Lie superalgebras. Adv. Math. 26, 8-96 (1977)
15. [K2] Kac, V.G.: Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula. Adv. Math. 30, 85-136 (1978)
16. [K3] Kac, V.G.: Infinite-dimensional Lie algebras. 3rd edition. Cambridge: Cambridge University Press, 1990
17. [K4] Kac, V.G.: Vertex algebras for beginners. Providence: AMS, University Lecture Series, Vol. 10, 1996. Second edition, 1998
18. [K5] Kac, V.G.: Classification of supersymmetries. ICM talk, August 2002
19. [KW1] Kac, V.G., Wakimoto, M.: Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. Proc. Natl. Acad. Sci. USA 85, 4956-4960 (1988)
20. [KW2] Kac, V.G., Wakimoto, M.: Classification of modular invariant representations of affine algebras. In: Infinite-dimensional Lie algebras and groups. Advanced Ser. Math. Phys. Vol. 7, Singapore: World Scientific, 1989, pp. 138-177
21. [KW3] Kac, V.G., Wakimoto, M.: Integrable highest weight modules over affine superalgebras and number theory. Progress in Math., 123, Boston: Birkhäuser, 1994, pp. 415-456
22. [KW4] Kac, V.G., Wakimoto, M.: Integrable highest weight modules over affine superalgebras and Appell's function. Commun. Math, Phys. 215, 631-682 (2001)
23. [KW5] Kac, V.G., Wakimoto, M.: Quantum reduction and representation theory of superconformal algebras, math-ph/0304011
24. [Kh] Khovanova, T.: Super K d V equation related to the Neveu-Schwarz-2 Lie superalgebra of string theory. Teor. Mat. Phys. 72, 306-312 (1987)
25. [Ki] Kiritsis, E.B.: Character formulae and the structure of the presentations of the N = 1, N = 2 superconformal algebras. Int. J. Mod. Phys. A. 3, 1871-1906 (1988)
26. [M] Matsuo, Y.: Character formula of C < 1 unitary representation of N = 2 superconformal algebra. Prog. Theor. Phys. 77, 793-797 (1987)
27. [RY] Ravanini, F., Yang, S-K.: Modular invariance in N = 2 superconformal field theories. Phys. Lett. B195, 202-208 (1987)
28. [R] Roan, S.S.: Heisenberg and modular invariance of N = 2 conformal field theory, Intern. J. Mod. Phys. A. 15, 3065-3094 (2000), hep-th/9902198
29. [W] Wakimoto, M.: Lectures on infinite-dimensional Lie algebra. Singapore: World Scientific, 2001