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Original Articles

Root Multiplicities of the Indefinite Kac–Moody Algebras of Symplectic Type

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Pages 764-782 | Received 17 Jul 2006, Published online: 07 Apr 2008

REFERENCES

  • Benkart , G. , Kang , S.-J. , Misra , K. C. ( 1993 ). Graded Lie algebras of Kac–Moody type . Adv. Math. 97 : 154 – 190 .
  • Benkart , G. , Kang , S.-J. , Misra , K. C. ( 1995 ). Indefinite Kac–Moody algebras of special linear type . Pacific J. Math. 170 : 379 – 404 .
  • Benkart , G. , Kang , S.-J. , Lee , H. , Shin , D. ( 1999 ). The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine Kac–Moody algebras . Contemporary Math. 248 : 1 – 29 .
  • Feingold , A. J. , Frenkel , I. B. ( 1983 ). A hyperbolic Kac–Moody algebra and the theory of Siegel modular forms of genus 2 . Math. Ann. 263 : 87 – 144 .
  • Frenkel , I. B. ( 1985 ). Representations of Kac–Moody algebras and dual resonance models, Applications of Group Theory in Physics and Mathematical Physics (Chicago, 1982), Lectures in Appl. Math. Vol. 21 , Providence , RI : Amer. Math. Soc. , pp. 325 – 353 .
  • Hontz , J. , Misra , K. C. ( 2002a ). Root multiplicities of the indefinite Kac–Moody Lie algebras and . Comm. Algebra 30 : 2941 – 2959 .
  • Hontz , J. , Misra , K. C. ( 2002b ). On root multiplicities of . Internat. J. Algebra Comput. 12 : 477 – 508 .
  • Kac , V. G. ( 1968 ). Simple irreducible graded Lie algebras of finite growth . Izv. Akad. Nauk SSSR Ser. Mat. 32 : 1323 – 1367 . ( Russian )
  • Kac , V. G. ( 1990 ). Infinite-Dimensional Lie Algebras, , 3rd ed. Cambridge : Cambridge University Press .
  • Kac , V. G. , Moody , R. V. , Wakimoto , M. ( 1988 ). On E10, Differential Geometrical Methods in Theoretical Physics (Como, 1987), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. Vol. 250 . Dordrecht : Kluwer Acad. Publ. , pp. 109 – 128 .
  • 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 Lie algebra . J. Algebra 160 : 492 – 523 .
  • Kang , S.-J . ( 1994a ). On the hyperbolic Kac–Moody Lie algebra . Trans. Amer. Math. Soc. 341 : 623 – 638 .
  • Kang , S.-J . ( 1994b ). Root multiplicities of Kac–Moody algebras . Duke Math. J. 74 : 635 – 666 .
  • Kang , S.-J. , Melville , D. J. ( 1994 ). Root Multiplicities of the Kac–Moody Algebras . J. Algebra 170 : 277 – 299 .
  • Kang , S.-J. , Kashiwara , M. , Misra , K. C. , Miwa , T. , Nakashima , T. , Nakayashiki , A. ( 1992a ). Affine crystals and vertex models, Infinite Analysis, Part A, B (Kyoto, 1991), Adv. Ser. Math. Phys. Vol. 16 , River Edge , NJ : World Sci. Publishing , pp. 449 – 484 .
  • Kang , S.-J. , Kashiwara , M. , Misra , K. C. , Miwa , T. , Nakashima , T. , Nakayashiki , A. ( 1992b ). Perfect crystals of quantum affine Lie algebras . Duke Math. J. 68 : 499 – 607 .
  • Kang , S.-J. , Kashiwara , M. , Misra , K. C. ( 1994 ). Crystal bases of Verma modules for quantum affine Lie algebras . Compositio Math. 92 : 299 – 325 .
  • Kashiwara , M. ( 1990 ). Crystalizing the q-analogue of universal enveloping algebras . Comm. Math. Phys. 133 : 249 – 260 .
  • Kashiwara , M. ( 1991 ). On crystal bases of the Q-analogue of universal enveloping algebras . Duke Math. J. 63 : 465 – 516 .
  • Kashiwara , M. ( 1993 ). The crystal base and Littelmanns refined Demazure character formula . Duke Math. J. 71 : 839 – 858 .
  • Communicated by J. Kuzmanovich.

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