Structure and Root MultiplicitiesReferences
- Benkart , G. M. , Kang , S. J. and Misra , K. C. 1993 . Graded Lie algebras of Kac–Moody type . Adv. Math. , 97 : 154 – 190 .
- Feingold , A. J. 1981 . Tensor product of certain modules for the generalized Cartan matrix Lie algebra . Comm. Algebra , 9 ( 12 ) : 1323 – 1341 .
- Feingold , A. J. and Frenkel , I. B. 1983 . A hyperbolic Kac–Moody algebra and the theory of siegal modular forms of genus 2 . Math. Ann. , 263 : 87 – 144 .
- Feingold , A. J. and Lepowsky , J. 1978 . The Weyl–Kac character formula and power series identities . Adv. Math. , 29 : 271 – 309 . [CROSSREF]
- Garland , G. and Lepowsky , J. 1976 . Lie algebra homology and the Macdonald–Kac formula . Invent. Math. , 34 : 37 – 76 .
- Kac , V. G. 1990 . Infinite Dimensional Lie Algebra , 3rd Cambridge : Cambridge University Press .
- Kac , V. G. , Moody , R. V. and Wakimoto , M. 1988 . “ On E 10 ” . In Differential Geometrical Methods in Theoretical Physics Edited by: Bleuler , K. and Werner , M. 109 – 128 . Kluwer Academic Publishers .
- Kang , S. J. 1993a . Kac–Moody Lie algebras, spectral sequences, and the Witt formula . Trans. Amer. Math. Soc. , 339 : 463 – 495 .
- Kang , S. J. 1993b . Root multiplicities of the hyperbolic Kac–Moody algebra . J. Algebra , 160 : 492 – 593 . [CROSSREF]
- Kang , S. J. 1994a . Root multiplicities of the hyperbolic Kac–Moody Lie algebra . J. Algebra , 170 : 277 – 299 . [CROSSREF]
- Kang , S. J. 1994b . On the hyperbolic Kac–Moody Lie algebra . Trans. Amer. Math. Soc. , 341 : 623 – 638 .
- Kang , S. J. and Kim , M. H. 1999 . Dimension formula for graded Lie algebras and its applications . Trans. Amer. Math. Soc. , 351 ( 11 ) : 4281 – 4336 . [CROSSREF]
- Kang , S. J. , Kashiwara , M. and Misra , K. C. 1994 . Crystal bases of Verma modules for quantum affine Lie algebras . Comp. Math. , 92 : 299 – 325 .
- Kang , S. J. , Kashiwara , M. , Misra , K. C. , Miwa , T. , Nakashima , T. and Nakayashiki , A. 1992 . Affine crystals and vertex models . Int. J. Modern Phys. , A7 ( Sppl. 1A ) : 449 – 484 . [CROSSREF]
- Liu , L. S. 1992 . Kostant's formula for Kac–Moody Lie algebras . J. Algebra , 149 : 155 – 178 . [CROSSREF]
- Sthanumoorthy , N. and Uma Maheswari , A. 1996a . Root multiplicities of extended hyperbolic Kac–Moody algebras . Comm. Algebra , 24 ( 14 ) : 4495 – 4512 .
- Sthanumoorthy , N. and Uma Maheswari , A. 1996b . Purely imaginary roots of Kac–Moody algebras . Comm. Algebra. , 24 ( 2 ) : 677 – 693 .
- Sthanumoorthy , N. , Lilly , P. L. and Uma Maheswari , A. 2004 . Root multiplicities of some classes of extended-hyperbolic Kac–Moody and extended-hyperbolic generalized Kac–Moody algebras. Contemporary Mathematics, AMS 343: 315–347
- #Communicated by K. Misra.