Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 2 Standard Modules for

REFERENCES

• Calinescu , C. ( 2008 ). Intertwining vertex operators and certain representations of . Commun. Contemp. Math. 10 : 47 – 79 .
   Web of Science ®Google Scholar
• Calinescu , C. ( 2007 ). Principal subspaces of higher-level standard -modules . J. Pure Appl. Algebra 210 : 559 – 575 .
   Web of Science ®Google Scholar
• Capparelli , S. , Lepowsky , J. , Milas , A. ( 2003 ). The Rogers–Ramanujan recursion and intertwining operators . Comm. Contemporary Math. 5 : 947 – 966 .
   Web of Science ®Google Scholar
• Capparelli , S. , Lepowsky , J. , Milas , A. ( 2006 ). The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators . Ramanujan J. 12 : 379 – 397 .
   Web of Science ®Google Scholar
• Dong , C. , Lepowsky , J. ( 1993 ). Generalized Vertex Algebras and Relative Vertex Operators . Progress in Math. Vol. 112 , Boston : Birkhaüser .
   Google Scholar
• Dong , C. , Li , H. , Mason , G. ( 1996 ). Simple currents and extensions of vertex operator algebras . Comm. Math. Physics 180 : 671 – 707 .
   Web of Science ®Google Scholar
• Fulton , W. , Harris , J. ( 1991 ). Representation Theory . Graduated Texts in Mathematics . New York : Springer-Verlag .
   Google Scholar
• Feigin , B. , Jimbo , M. , Loktev , S. , Miwa , T. , Mukhin , E. ( 2003 ). Bosonic formulas for (k, ℓ)-admissible partitions . Ramanujan J. 7 : 485 – 517 ; Addendum to ‘Bosonic formulas for (k, ℓ)-admissible partitions', Ramanujan J. 7:519–530 .
   Google Scholar
• Frenkel , I. , Kac , V. ( 1980 ). Basic representations of affine Lie algebras and dual resonance models . Invent. Math. 62 : 23 – 66 .
   Web of Science ®Google Scholar
• Frenkel , I. , Lepowsky , J. , Meurman , A. ( 1988 ). Vertex Operator Algebras and the Monster . Pure and Appl. Math. 134 . Boston : Academic Press .
   Google Scholar
• 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 Feigin, B., Stoyanovsky, A. Quasi-particles models for the representations of Lie algebras and geometry of flag manifold. hep-th/9308079, RIMS 942 .
   Google Scholar
• Georgiev , G. (1996). Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace. J. Pure Appl. Algebra 112:247–286.
   Web of Science ®Google Scholar
• Humphreys , J. E. ( 1972 ). Introduction to Lie Algebras and Representation Theory . Graduated Texts in Mathematics . New York : Springer-Verlag .
   Google Scholar
• Jerković , M. ( 2009 ). Recurrence relations for characters of affine Lie algebra . J. Pure Appl. Algebra 213 : 913 – 926 .
   Google Scholar
• Kac , V. G. ( 1990 ). Infinite-Dimensional Lie Algebras. , 3rd ed. Cambridge : Cambridge University Press .
   Google Scholar
• 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 Vol. 7, Suppl. 1A, Proceedings of the RIMS Research Project 1991, “Infinite Analysis,” Singapore: World Scientific, pp. 449–484 .
   Google Scholar
• Lepowsky , J. , Li , H.-S. ( 2004 ). Introduction to Vertex Operator Algebras and Their Representations . Progress in Math . Vol. 227 . Boston : Birkhäuser .
   Google Scholar
• Lepowsky , J. , Primc , M. ( 1985 ). Structure of the standard modules for the affine Lie algebra . Contemporary Math. 46 : 1 – 84 .
   Google Scholar
• Lepowsky , J. , Wilson , R. L. ( 1984 ). The structure of standard modules, I: Universal algebras and the Rogers–Ramanujan identities . Invent. Math. 77 : 199 – 290 .
   Web of Science ®Google Scholar
• Lepowsky , J. , Wilson , R. L. ( 1985 ). The structure of standard modules, II: The case , principal gradation . Invent. Math. 79 : 417 – 442 .
   Web of Science ®Google Scholar
• Primc , M. ( 1994 ). Vertex operator construction of standard modules for . Pacific J. Math. 162 : 143 – 187 .
   Web of Science ®Google Scholar
• Primc , M. ( 2000 ). Basic Representations for classical affine Lie algebras . J. Algebra 228 : 1 – 50 .
   Web of Science ®Google Scholar
• Primc , M. (k, r)-admissible configurations and intertwining operators . Contemp. Math. 442 : 425 – 434 .
   Google Scholar
• Segal , G. ( 1981 ). Unitary representations of some infinite-dimensional groups . Commun. Math. Phys. 80 : 301 – 342 .
   Web of Science ®Google Scholar
• Trupčević , G. Combinatorial bases of Feigin–Stoyanovsky's type subspace of level 1 standard 𝔰𝔩(ℓ +1, ℂ)-modules, arXiv: 1002.0348. 22 July 2008 .
   Google Scholar
• Trupčević , G. ( 2009 ). Combinatorial bases of Feigin–Stoyanovsky's type subspaces of higher-level standard -modules . J. Algebra 322 ( 10 ): 3744 – 3774 .
   Google Scholar
• Communicated by K. Misra.
   Google Scholar