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2012 | 10 | 2 | 703-721

Tytuł artykułu

Quasi-particle fermionic formulas for (k, 3)-admissible configurations

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Abstrakty

EN
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.

Twórcy

  • University of Zagreb
autor
  • University of Zagreb

Bibliografia

  • [1] Ardonne E., Kedem R., Stone M., Fermionic characters and arbitrary highest-weight integrable bs \(\widehat{\mathfrak{s}l}_{r + 1}\) -modules, Comm. Math. Phys., 2006, 264(2), 427–464 http://dx.doi.org/10.1007/s00220-005-1486-3
  • [2] Baranović I., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level 2 standard modules for D 4(1), Comm. Algebra, 2011, 39(3), 1007–1051 http://dx.doi.org/10.1080/00927871003639329
  • [3] Calinescu C., Principal subspaces of higher-level standard \(\widehat{\mathfrak{s}\mathfrak{l}(3)}\) -modules, J. Pure Appl. Algebra, 2007, 210(2), 559–575 http://dx.doi.org/10.1016/j.jpaa.2006.10.018
  • [4] Calinescu C., Intertwining vertex operators and certain representations of \(\widehat{\mathfrak{s}\mathfrak{l}(n)}\) , Commun. Contemp. Math., 2008, 10(1), 47–79 http://dx.doi.org/10.1142/S0219199708002703
  • [5] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of certain A 1(1)-modules I: Level one case, Internat. J. Math., 2008, 19(1), 71–92 http://dx.doi.org/10.1142/S0129167X08004571
  • [6] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of certain A 1(1)-modules II: Higher-level case, J. Pure Appl. Algebra, 2008, 212(8), 1928–1950 http://dx.doi.org/10.1016/j.jpaa.2008.01.003
  • [7] Calinescu C., Lepowsky J., Milas A., Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A, D, E, J. Algebra, 2010, 323(1), 167–192 http://dx.doi.org/10.1016/j.jalgebra.2009.09.029
  • [8] Capparelli S., Lepowsky J., Milas A., The Rogers-Ramanujan recursion and intertwining operators, Commun. Contemp. Math., 2003, 5(6), 947–966 http://dx.doi.org/10.1142/S0219199703001191
  • [9] Capparelli S., Lepowsky J., Milas A., The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators, Ramanujan J., 2006, 12(3), 379–397 http://dx.doi.org/10.1007/s11139-006-0150-7
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  • [11] Feigin B., Jimbo M., Loktev S., Miwa T., Mukhin E., Bosonic formulas for (k; l)-admissible partitions, Ramanujan J., 2003, 7(4), 485–517, 519–530 http://dx.doi.org/10.1023/B:RAMA.0000012430.68976.c0
  • [12] Feigin B., Jimbo M., Miwa T., Mukhin E., Takeyama Y., Fermionic formulas for (k; 3)-admissible configurations, Publ. Res. Inst. Math. Sci., 2004, 40(1), 125–162 http://dx.doi.org/10.2977/prims/1145475968
  • [13] Feigin B., Jimbo M., Miwa T., Mukhin E., Takeyama Y., Particle content of the (k; 3)-configurations, Publ. Res. Inst. Math. Sci., 2004, 40(1), 163–220 http://dx.doi.org/10.2977/prims/1145475969
  • [14] Frenkel I.B., Kac V.G., Basic representations of affine Lie algebras and dual resonance models, Invent. Math., 1980, 62(1), 23–66 http://dx.doi.org/10.1007/BF01391662
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  • [17] Jerković M., Recurrence relations for characters of affine Lie algebra A ℓ(1), J. Pure Appl. Algebra, 2009, 213(6), 913–926 http://dx.doi.org/10.1016/j.jpaa.2008.10.001
  • [18] Jerković M., Recurrences and characters of Feigin-Stoyanovsky’s type subspaces, In: Vertex Operator Algebras and Related Areas, Contemp. Math., 497, American Mathematical Society, Providence, 2009, 113–123
  • [19] Jerković M., Character formulas for Feigin-Stoyanovsky’s type subspaces of standard sl(3, ℂ)∧-modules, preprint avaliable at http://arxiv.org/abs/1105.2927
  • [20] Kac V.G., Infinite-Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9780511626234
  • [21] Lepowsky J., Wilson R.L., The structure of standard modules I. Universal algebras and the Rogers-Ramanujan identities, Invent. Math., 1984, 77(2), 199–290; The structure of standard modules II. The case A 1(1), principal gradation, Invent. Math., 1985, 79(5), 417–442 http://dx.doi.org/10.1007/BF01388447
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  • [23] Primc M., (k; r)-admissible configurations and intertwining operators, In: Lie Algebras, Vertex Operator Algebras and their Applications, Contemp. Math., 442, American Mathematical Society, Providence, 2007, 425–434
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  • [25] Stoyanovsky A.V., Feigin B.L., Functional models of the representations of current algebras, and semi-infinite Schubert cells, Funktsional. Anal. i Prilozhen., 1994, 28(1), 68–90 (in Russian) http://dx.doi.org/10.1007/BF01079010
  • [26] Trupčević G., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of higher-level standard \(\mathop {\mathfrak{s}l}\limits^ \sim (\ell + 1,\mathbb{C})\) -modules, J. Algebra, 2009, 322(10), 3744–3774 http://dx.doi.org/10.1016/j.jalgebra.2009.07.024
  • [27] Trupčević G., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level 1 standard modules for \(\mathop {\mathfrak{s}l}\limits^ \sim (\ell + 1,\mathbb{C})\) , Comm. Algebra, 2010, 38(10), 3913–3940 http://dx.doi.org/10.1080/00927870903366827

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