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Original Articles

Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 1 Standard Modules for

Pages 3913-3940 | Received 29 Oct 2008, Published online: 24 Nov 2010

REFERENCES

  • Calinescu , C. ( 2008 ). Intertwining vertex operators and certain representations of . Comm. Contemp. Math. 10 : 47 – 79 .
  • Calinescu , C. ( 2007 ). Principal subspaces of higher-level standard -modules . J. Pure Appl. Algebra 210 : 559 – 575 .
  • Calinescu , C. , Lepowsky , J. , Milas , A. ( 2008a ). Vertex-algebraic structure of the principal subspaces of certain -modules, I: level one case . Int. J. Math. 19 : 71 – 92 .
  • Calinescu , C. , Lepowsky , J. , Milas , A. ( 2008b ). Vertex-algebraic structure of the principal subspaces of certain -modules, II: higher-level case . J. Pure Appl. Algebra 212 : 1928 – 1950 .
  • Capparelli , S. , Lepowsky , J. , Milas , A. (2003). The Rogers–Ramanujan recursion and intertwining operators. Comm. Contemp. Math. 5:947–966.
  • Capparelli , S. , Lepowsky , J. , Milas , A. ( 2006 ). The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators . Ramanujan J. 12 ( 3 ): 379 – 397 .
  • Dong , C. , Lepowsky , J. ( 1993 ). Generalized Vertex Algebras and Relative Vertex Operators . Progress in Math. 112 , Boston : Birkhaüser .
  • Feigin , B. , Jimbo , M. , Loktev , S. , Miwa , T. , Mukhin , E. ( 2003 ). Bosonic formulas for (k, ℓ)-admissible partitions . Ramanujan J. 7(4):485–517.; Addendum to ‘Bosonic formulas for (k, ℓ)-admissible partitions'. Ramanujan J. 7 : 519 – 530 .
  • Feigin , B. , Jimbo , M. , Miwa , T. , Mukhin , E. , Takeyama , Y. ( 2004a ). Fermionic formulas for (k, 3)-admissible configurations . Publ. RIMS 40 : 125 – 162 .
  • Feigin , B. , Jimbo , M. , Miwa , T. , Mukhin , E. , Takeyama , Y. ( 2004b ). Particle content of the (k, 3)-configurations . Publ. RIMS 40 : 163 – 220 .
  • Stoyanovsky , A. V. , Feigin , B. L. ( 1994 ). Functional models of the representations of current algebras, and semi-infinite Schubert cells. (Russian) Funktsional. Anal. i Prilozhen. 28:68–90, 96; translation in Funct. Anal. Appl. 28:55–72; preprint B. Feigin and A. Stoyanovsky, Quasi-Particles Models for the Representations of Lie Algebras and Geometry of Flag Manifold, hep-th/9308079, RIMS 942 .
  • Frenkel , I. , Kac , V. ( 1980 ). Basic representations of affine Lie algebras and dual resonance models . Invent. Math. 62 : 23 – 66 .
  • Frenkel , I. , Lepowsky , J. , Meurman , A. ( 1988 ). Vertex operator algebras and the monster. Pure and Appl. Math. Vol. 134, Boston: Academic Press .
  • Georgiev , G. ( 1996 ). Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace . J. Pure Appl. Algebra 112 : 247 – 286 .
  • Jerković , M. ( 2009 ). Recurrence relations for characters of affine Lie algebra . J. Pure Appl. Algebra 213 : 913 – 926 .
  • Kac , V. G. ( 1990 ). Infinite-Dimensional Lie Algebras. , 3rd ed. Cambridge : Cambridge University Press .
  • Kang , S.-J. , Kashiwara , M. , Misra , K. C. , Miwa , T. , Nakashima , T. , Nakayashiki , A. ( 1992 ). Affine crystals and vertex models. International Journal of Modern Physics A 7, Suppl. 1A, Proceedings of the RIMS Research Project 1991, “Infinite Analysis”, Singapore: World Scientific, pp. 449–484 .
  • Lepowsky , J. , Li , H.-S. ( 2004 ). Introduction to vertex operator algebras and their representations. Progress in Math. 227, Boston: Birkhäuser .
  • Lepowsky , J. , Primc , M. ( 1985 ). Structure of the standard modules for the affine Lie algebra . Contemporary Math. 46 : 1 – 84 .
  • Lepowsky , J. , Wilson , R. L. ( 1984 ). The structure of standard modules, I: Universal algebras and the Rogers–Ramanujan identities . Invent. Math. 77 : 199 – 290 .
  • Meurman , A. , Primc , M. ( 1999 ). Annihilating fields of standard modules of and combinatorial identities. Memoirs Amer. Math. Soc. 652 .
  • Primc , M. ( 1994 ). Vertex operator construction of standard modules for . Pacific J. Math. 162 : 143 – 187 .
  • Primc , M. ( 2000 ). Basic representations sor classical affine Lie algebras . J. Algebra 228 : 1 – 50 .
  • Primc , M. ( 2007 ). (k, r)-admissible configurations and intertwining operators . Contemporary Math. 442 : 425 – 434 .
  • Segal , G. ( 1981 ). Unitary representations of some infinite-dimensional groups . Commun. Math. Phys. 80 : 301 – 342 .
  • Trupčević , G. ( 2009 ). Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard -modules . J. Algebra 322 : 3744 – 3774 .
  • Communicated by K. Misra.

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