References
D. Adamovic and A. Milas, “Vertex operator algebras associated to modular invariant representations forA 11 ,” Math. Res. Lett.,2, No. 3, 563–575 (1995).
H. Andersen and J. Paradowski, “Fusion categories arising from semi-simple Lie algebras,” Commun. Math. Phys.,169, 563–588 (1995).
J. N. Bernstein and S. I. Gelfand, “Tensor products of finite and infinite dimensional representations of semi-simple Lie algebras,” Compositio Math.,41, No. 2, 245–285 (1980).
V. V. Deodhar, O. Gabber, and V. G. Kac, “Structure of some categories of representations of infinite dimensional Lie algebras,” Adv. Math.,45, 92–116 (1982).
V. G. Drinfeld, “On quasitriangular quasi-Hopf algebras and on a group that is closely connected with\(Gal(\bar Q/Q)\),” Algebra Analiz,2, No. 4, 149–181 (1990); English transl. in Leningrad Math. J.,2, No. 4, 829–860 (1991).
C. Dong, H. Li, and G. Mason, Vertex Operator Algebras Associated to Admissible Representations of\(\widehat{sl}_2 \), Preprint q-algebra/9509026.
M. Duflo, “Representations irreductibles des groupes semi-simples complexes,” In: Lect. Notes Math., Vol. 497, Springer-Verlag, 1975, pp. 26–88.
T. Enright, “On the irreducibility of the fundamental series of a real semi-simple Lie algebra,” Ann. Math.,110, 1–82 (1979).
B. Feigin and E. Frenkel, “Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras,” Int. J. Math. Phys. A,7, Supplement1A, 197–215 (1992).
B. Feigin and F. Malikov, “Fusion algebras and cohomology of a nilpotent subalgebra of an affine Lie algebra,” Lett. Math. Phys.,31, 315–325 (1994).
B. Feigin and F. Malikov, “Modular functor and representation theory of\(\widehat{sl}_2 \) at a rational level,” In: “Operads: Proceedings of Renaissance Conferences,” Contemp. Math., Vol. 202 (J-L. Loday, J. Stasheff, and A. Voronov, eds.), 1997.
M. Finkelberg, Fusion Categories, Ph.D. Thesis, Harvard University, 1993.
E. Frenkel, V. Kac, and M. Wakimoto, “Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction,” Commun. Math. Phys.,147, 295–328 (1992).
I. B. Frenkel, J. Lepowsky, and A. Meurman, Vertex Operator Algebras and the Monster, Academic Press, 1988.
I. B. Frenkel and Y. Zhu, “Vertex operator algebras associated to representations of affine and Virasoro algebras,” Duke Math. J.,66, 123–168 (1992).
J. C. Jantzen, Moduln mit einem hoschten Gewicht, Lect. Notes Math., Vol. 750, Springer-Verlag, 1979.
J. C. Jantzen, Representations of Algebraic Groups, Pure Appl. Math., Vol. 131, Academic Press, 1987.
A. Joseph, “Dixmier’s problem for Verma and principal series submodules,” J. London Math. Soc. (2),20, No. 2, 193–204 (1979).
V. G. Kac and D. A. Kazhdan, “Structure of representations with highest weight of infinite dimensional Lie algebras,” Adv. Math.,34, 97–108 (1979).
V. G. Kac and M. Wakimoto, “Modular invariant representations of infinite dimensional Lie algebras and superalgebras,” Proc. Natl. Acad. Sci. U.S.A.,85, No. 14, 4956–4960 (1988).
D. Kazhdan and G. Lusztig, “Affine Lie algebras and quantum groups,” Internat. Math. Res. Notices, No. 2, 21–29 (1991).
D. Kazhdan and G. Lusztig, “Tensor structures arising from affine algebras. I, II,” J. Amer. Math. Soc.,6, No. 4, 905–947 949–1011 (1993).
D. Kazhdan and G. Lusztig, “Tensor structures arising from affine algebras. III, IV,” J. Amer. Math. Soc.,7, No. 2, 335–381, 383–453 (1994).
G. Lusztig, “Nonlocal finiteness of aW-graph,” Electronic J. Representation Theory,1, 25–30 (1997).
I. Mircovič, unpublished.
C. M. Ringel, “The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences,” Math. Z.208, 209–223 (1991).
A. Rocha and N. Wallach, “Projective modules over graded Lie algebras I,” Math. Z.,180, 151–177 (1982).
D. Vogan, “Irreducible characters of semi-simple Lie groups,” Duke Math. J.,46, 61–108, 805–859 (1979).
G. Zuckerman, “Tensor products of finite and infinite dimensional representations of semi-simple Lie groups,” Ann. Math.,106, 295–308 (1977).
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Department of Mathematics, Yale University; Department of Mathematics, University of Southern California. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 2, pp. 31–42, April–June, 1999.
Translated by I. B. Frenkel and F. G. Malikov
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Frenkel, I.B., Malikov, F.G. Annihilating ideals and tilting functors. Funct Anal Its Appl 33, 106–115 (1999). https://doi.org/10.1007/BF02465191
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DOI: https://doi.org/10.1007/BF02465191