On some modular representations of affine Kac-Moody algebras at the critical level
Mathieu, Olivier
Compositio Mathematica, Tome 104 (1996), p. 305-312 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1996-01-01
@article{CM_1996__102_3_305_0,
     author = {Mathieu, Olivier},
     title = {On some modular representations of affine Kac-Moody algebras at the critical level},
     journal = {Compositio Mathematica},
     volume = {104},
     year = {1996},
     pages = {305-312},
     mrnumber = {1401425},
     zbl = {0878.17023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1996__102_3_305_0}
}

Mathieu, Olivier. On some modular representations of affine Kac-Moody algebras at the critical level. Compositio Mathematica, Tome 104 (1996) pp. 305-312. http://gdmltest.u-ga.fr/item/CM_1996__102_3_305_0/

[DGK] Deodhar, V., Gabber, O. and Kac, V.: Structure of some categories of representations of infinite dimensional Lie algebras, Adv. in Math. 89 (1987) 247-270. | MR 663417 | Zbl 0491.17008

[FF1] Feigin, B. and Frenkel, E.: The family of representations of affine Lie algebras, Russian Math. Survey 43 (1988) 221-222. | MR 971497 | Zbl 0668.17015

[FF2] Feigin, B. and Frenkel, E.: Affine Kac-Moody algebras and semi-infinite flag, Comm. Math. Phys. 128 (1990) 161-189. | MR 1042449 | Zbl 0722.17019

[FF3] Feigin, B. and Frenkel, E.: Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras, Int. J. Math. Phys. A7 (1992) 197-215. | MR 1187549 | Zbl 0925.17022

[F] Frenkel, E.: Affine Kac-Moody Algebras at the Critical Level and Quantum Drinfeld-Sokolov Reduction, Harvard Thesis 1990.

[GW] Goodman, R. and Wallach, N.: Higher order Sugawara operators for affine Kac-Moody algebras, Trans. A.M.S. 315 (1989) 1-66. | MR 958893 | Zbl 0676.17013

[H] Hayashi, T.: Sugawara operators and Kac-Kazdhan conjecture, Inv. Math. 94 (1988) 13-52. | MR 958588 | Zbl 0674.17005

[J] Jacobson, N.: Lie Algebras, New York, Interscience (1962). | MR 143793 | Zbl 0121.27504

[K] Kac, V.G.: Infinite dimensional Lie algebras, Birkhauser, Prog. in Math. 44 (1983). | MR 739850 | Zbl 0537.17001

[KK] Kac, V.G. and Kazdhan, D.: Structure of representations with highest weight of infinite dimensional Lie algebras, Adv. Math. 34 (1979) 97-108. | MR 547842 | Zbl 0427.17011

[Ku] Ku, J.M.: Structure of the module M(-p) for euclidean Lie algebras, J. ofAlg. 124 (1989) 367-387. | MR 1011602 | Zbl 0693.17013

[M1] Malikov, F.: Singular vectors corresponding to imaginary roots in Verma modules over affine Lie algebras, Math. Scan. 66 (1986) 73-90. | MR 1060899 | Zbl 0687.17009

[Mt1] Mathieu, O.: Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque (1988) 159-160. | MR 980506 | Zbl 0683.17010

[Mt2] Mathieu, O.: Construction du groupe de Kac-Moody et applications, Comp. Math. 69 (1989) 37-60. | Numdam | MR 986812 | Zbl 0678.17012

[Mt3] Mathieu, O.: Bicontinuity of the Dixmier map, Journal of the A.M.S. 4 (1991) 837-863. | MR 1115787 | Zbl 0743.17013

[Mt 4] Mathieu, O.: On the endomorphism ring of some modular Verma modules at the critical level, Preprint.

[T 1] Tits, J.: Groups and group functions attached to Kac-Moody data, Springer-Verlag, Lect. Notes in Math. 111 (1985) 193-223. | MR 797422 | Zbl 0572.17010

[T 2] Tits, J.: Groupes et Algèbres de Kac-Moody, Résumé de cours, Collége de France (1982-1983).

[Wt] Wakimoto, M.: Fock representation of the affine Lie algebra A1(1), Comm. Math. Phys. 104 (1986) 604-609. | MR 841673 | Zbl 0587.17009