Kazhdan-lusztig conjecture for generalized kac-moody algebras, I: towards the conjecture

References

• Beilinson , A. and Bernstein , J. 1981 . Localisation de Q-modules . C. R. Acad. Sci. Paris , 292 : 15 – 18 .
   Google Scholar
• Borcherds , R. E. 1988 . Generalized Kac-Moody algebras . J. Algebra , 115 : 501 – 512 .
   Web of Science ®Google Scholar
• Borcherds , R. E. 1990 . The monster Lie algebra . Adv. Math , 83 : 30 – 47 .
   Web of Science ®Google Scholar
• Borcherds , R. E. 1991 . Central extensions of generalized Kac-Moody algebras . J. Algebra , 140 : 330 – 335 .
   Google Scholar
• Borcherds , R. E. 1992 . Monstrous moonshine and monstrous Lie superalgebras . Invent. Math , 109 : 405 – 444 .
   Web of Science ®Google Scholar
• Brylinski , J.-L and Kashiwara , M. 1981 . Kazhdan-Lusztig conjecture and holonomic systems . Invent. Math , 64 : 387 – 410 .
   Web of Science ®Google Scholar
• Casian , L. 1990 . Kazhdan-Lusztig multiplicity formulas for Kac-Moody algebras . C. R. Acad. Sci. Paris , 310 : 333 – 337 .
   PubMedGoogle Scholar
• Deodhar , V. V. , Gabber , O. and Kac , V. G. 1982 . Structure of some categories of representations of infinite-dimensional Lie algebras . Adv. Math , 45 : 92 – 116 .
   Web of Science ®Google Scholar
• Garland , H. and Lepowsky , J. 1976 . Lie algebra homology and the Macdonald-Kac formulas . Invent. Math , 34 : 37 – 76 .
   Web of Science ®Google Scholar
• Harada , K. , Miyamoto , M. and Yamada , H. A generalization of Kac-Moody algebras
   Google Scholar
• Jantzen , J. C. 1979 . Moduln mit einem hochsten Gewicht . Lecture Notes in Math , 750
   Google Scholar
• Kac , V. G. 1990 . Infinite Dimensional Lie Algebras (3rd ed.) , Cambridge : Cambridge Univ. Press .
   Google Scholar
• Kang , S.J. 1994 . Generalized Kac-Moody algebras and the modular function j . Math, Ann , 298 : 373 – 384 .
   Web of Science ®Google Scholar
• Kashiwara , M. 1990 . Kazhdan-Lusztig conjecture for a symmetrizable Kac-Moody Lie algebra . The Grothendieck Festschrift, Volume II , 87 : 407 – 433 .
   Google Scholar
• Kashiwara , M. and Tanisaki , T. 1990 . Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebra, II: Intersection cohomologies of Schubert varieties . Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory , 92 : 159 – 195 .
   Google Scholar
• Kazhdan , D. and Lusztig , G. 1979 . Representations of Coxeter groups and Heche algebras . Invent. Math , 53 : 165 – 184 .
   Web of Science ®Google Scholar
• Kazhdan , D. and Lusztig , G. 1980 . Schubert varieties and Poincare duality . Proc. Sympos. Pure Math , 36 : 185 – 203 .
   Google Scholar
• Naito , S. 1993 . The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras, I: The existence of the resolution . Publ. Res. Inst. Math. Sci , 29 : 709 – 730 .
   Google Scholar
• Naito , S. 1994 . The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras, II: An explicit construction of the resolution . J. Algebra , 167 : 778 – 802 .
   Google Scholar
• Neidhardt , W. 1987 . A translation principle for Kac-Moody algebras . Proc. Amer. Math. Soc , 100 : 395 – 400 .
   Google Scholar
• A. Rocha , Caridi and Wallach , N. R. 1982 . Projective modules over graded Lie algebras. / . Math. Z , 180 : 151 – 177 .
   Google Scholar
• A. Rocha , Caridi and Wallach , N. R. 1983 . Wallach, Highest weight modules over graded Lie algebras: Resolutions, filtrations and character formulas . IVans. Amer. Math. Soc , 277 : 133 – 162 .
   Google Scholar
• Suto , K. 1987 . On the Kazhdan-Lusztig conjecture for Kac-Moody algebras . J. Math. Kyoto Univ , 27 : 243 – 258 .
   Google Scholar