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Original Articles

Quantum z-algebras and representations of quantum affine algebras

Pages 829-844 | Received 01 Sep 1998, Published online: 27 Jun 2007

References

  • Abada , A. , Bougourzi , A.H. and Gradechi , E.L. 1993 . Deformation of Wakimoto construction . Mod. Phys. Lett , A8 : 715 – 724 .
  • Awata , H. , Odake , S. and Shiraishi , J. 1994 . Free boson representation of Uq(ŝlN) . Comrnun. Math. Phys , A8 : 61 – 83 .
  • Beck , J. 1994 . Braid group action and quantum affine algebras . Commun. Math. Phys , 165 : 555 – 568 .
  • Bernard , D. 1989 . Vertex operator representations of quantum affine algebras Uq(B(1) . Lett. Math. Phys , 17 : 239 – 245 .
  • Bougourzi , A.H. 1993 . Uniqueness of the bosonization of the Uq(su(2)k) quantum current algebra . Nucl. Phys , B404 : 457 – 482 .
  • Bougourzi , A.H. and Vinet , H. 1996 . A quantum analogue of the Z algebra . J. Math. Phys , 37 : 3548 – 3567 .
  • Ding , J. and Feigin , B. 1997 . Quantum current operators. II. Difference equations of quantum current operators and quantum parafermion construction , Vol. 33 , 285 – 300 . Publ. Res. Inst. Math. Sci .
  • Ding , J. and Frenkel , I.B. 1993 . Isomorphisms of two constructions of quantum affine algebras . Comm. Math. Phys , 156 : 277 – 300 .
  • Ding , J. and Miwa , T. 1997 . Quantum current operators. I. Zeros and poles of quantum current operators and the condition of quantum integrability , Vol. 33 , 277 – 284 . Publ. Res. Inst. Math. Sci .
  • Drinfeld , V.G. 1997 . New realization of Yangians and quantum affine algebras . Sov. Math. Dokl , 36 : 212 – 216 .
  • Frenkel , I.B. and Jing , N. 1988 . Vertex representations of quantum affine algebras , Vol. 85 , 9373 – 9377 . USA : Proc. Nat’l Acad .
  • Frenkel , I. , Lepowsky , J. and Meurman , A. 1988 . Vertex operator algebras and the Monster , New York : Academic Press .
  • Jing , N. 1990 . Twisted vertex representations of quantum affine algebras . Invent. Math , 102 : 663 – 690 .
  • Jing , N. 1996 . Higher level representations of the quantum affine algebra Uq(ŝl2) . Jour. Alg , 182 : 448 – 468 .
  • Jing , N. 1999 . Level one representations of . Proc. Amer. Math. Soc , 127 : 21 – 27 .
  • Jing , N. . On Drinfeld realization of quantum affine algebras . Proc. Lie algebras and the Monster . Edited by: Ferrar , J. and Harada , K. Vol. 7 , pp. 195 – 206 . Berlin : De Gruyter . Ohio State Univ. Math. Res. Inst. Publ
  • Jing N. New twisted quantum current algebras math.QA/9901066
  • Jing , N. and Misra , K.C. 1996 . Vertex operators of level one -modules . Lett. Math. Phys , 36 : 127 – 143 .
  • Jing , N. , Koyania , Y. and Misra , K.C. 1998 . Bosonic realizations of . Jour. Algebra , 200 : 155 – 172 .
  • Jing N. Koyama Y. Misra K.C. Level one realizations of quantum affine algebras math.QA/9802123)
  • Idzumi , M. 1994 . Level two irreducible representations of Uq(ŝl 2) . Int. J. Mod. Phys , A9 : 4449 – 4484 .
  • Kac , V.G. 1990 . Infinite dimensional Lie algebras , Cambridge University Press .
  • Kashiwara , M. , Miwa , T. , Peterson , J.U.H. and Yung , C.M. 1996 . Perfect crystals and q-deformed Fock spaces . Selecta Mathematica , 2 : 415 – 499 .
  • Lepowsky , J. and Prime , M. 1984 . “ Standard modules for type one affine Lie algebras ” . In Number Theory , Vol. 1052 , 194 – 251 . New York : Springer-Verlag . Lect. Notes in Math
  • Lepowsky , J. and Prime , M. 1985 . “ Structure of the standard modules for the affine Lie algebra ” . In Contemporary Math , Vol. 46 , Providence, RI : Amer. Math. Soc .
  • Lepowsky , J. and Wilson , R.L. 1981 . A new family of algebras underlying the Rogers-Ramanu- jan identities and generalizations , Vol. 78 , 7254 – 7258 . USA : Proc. Nat’l. Acad. Sci .
  • Lepowsky , J. and Wilson , R.L. 1984 . The structure of standard modules, I:Universal algebras and the Rogers-Ramanujan identities . Invent. Math , 77 : 199 – 290 .
  • Lepowsky , J. and Wilson , R.L. 1985 . The structure of standard modules, II:The case principal gradation . Invent. Math , 77 : 417 – 442 .
  • Matsuo , A. 1994 . A q-deformation of Wakimoto modules, primary fields and screening oper-ators . Comm. Math. Phys , 160 : 33 – 48 .
  • Misra , K.C. 1991 . Level two standard à n -modules . J. Alg , 137 : 56 – 76 .
  • Prime , M. 1989 . “ Standard representations of ” . In Infinite-dimensional Lie algebras and groups , 273 – 284 . Singapore : World Sci. Singapore .
  • Shiraishi , J. 1992 . Free boson representation of Uq(ŝl2) . Phys. Lett , A171 : 243 – 248 .

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