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2013 | 11 | 2 | 197-225

Tytuł artykułu

Combinatorial bases of modules for affine Lie algebra B 2(1)

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Abstrakty

EN
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.

Twórcy

autor
  • University of Zagreb

Bibliografia

  • [1] Ardonne E., Kedem R., Stone M., Fermionic characters and arbitrary highest-weight integrable \( \widehat{\mathfrak{s}\mathfrak{l}}_{r + 1} \) -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., 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
  • [5] 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
  • [6] 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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  • [24] Meurman A., Primc M., Vertex operator algebras and representations of affine Lie algebras, Acta Appl. Math., 1996, 44(1–2), 207–215 http://dx.doi.org/10.1007/BF00116522
  • [25] Meurman A., Primc M., Annihilating Fields of Standard Modules of sl(2,ℂ)∼ and Combinatorial Identities, Mem. Amer. Math. Soc., 1999, 137, #652
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  • [28] Primc M., (k, r)-admissible configurations and intertwining operators, In: Lie Algebras, Vertex Operator Algebras and Their Applications, Raleigh, May 17–21, 2005, Contemp. Math., 442, American Mathematical Society, Providence, 2007, 425–434 http://dx.doi.org/10.1090/conm/442/08540
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  • [30] Trupčević G., Combinatorial bases of Feigin-Stoyanovsky’s type subspaces of higher-level standard \( \widetilde{\mathfrak{s}\mathfrak{l}}(\ell + 1,\mathbb{C}) \) -modules, J. Algebra, 2009, 322(10), 3744–3774 http://dx.doi.org/10.1016/j.jalgebra.2009.07.024

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