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2013 | 11 | 1 | 1-16
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The 3-state Potts model and Rogers-Ramanujan series

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Języki publikacji
EN
Abstrakty
EN
We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
1
Strony
1-16
Opis fizyczny
Daty
wydano
2013-01-01
online
2012-10-24
Twórcy
autor
Bibliografia
  • [1] Adamovic D., Perše O., On coset vertex algebras with central charge 1, Math. Commun., 2010, 15(1), 143–157
  • [2] Arakawa T., Representation theory of W-algebras, Invent. Math., 2007, 169(2), 219–320 http://dx.doi.org/10.1007/s00222-007-0046-1
  • [3] Bais F.A., Bouwknegt P., Surridge M., Schoutens K., Coset construction for extended Virasoro algebras, Nuclear Phys. B, 1988, 304(2), 371–391 http://dx.doi.org/10.1016/0550-3213(88)90632-3
  • [4] Borcea J., Dualities, Affine Vertex Operator Algebras, and Geometry of Complex Polynomials, PhD thesis, Lund University, 1998
  • [5] Bouwknegt P., Schoutens K., W-symmetry in conformal field theory, Phys. Rep., 1993, 223(4), 183–276 http://dx.doi.org/10.1016/0370-1573(93)90111-P
  • [6] Bytsko A., Fring A., Factorized combinations of Virasoro characters, Comm. Math. Phys., 2000, 209(1), 179–205 http://dx.doi.org/10.1007/s002200050019
  • [7] Capparelli S., A combinatorial proof of a partition identity related to the level 3 representations of a twisted affine Lie algebra, Comm. Algebra, 1995, 23(8), 2959–2969 http://dx.doi.org/10.1080/00927879508825379
  • [8] Dong C., Li H., Mason G., Twisted representations of vertex operator algebras and associative algebras, Internat. Math. Res. Notices, 1998, 8, 389–397 http://dx.doi.org/10.1155/S1073792898000269
  • [9] Dong C., Li H., Mason G., Modular-invariance of trace functions in orbifold theory and generalized Moonshine, Comm. Math. Phys., 2000, 214(1), 1–56 http://dx.doi.org/10.1007/s002200000242
  • [10] Dong C., Wang Q., On C 2-cofiniteness of parafermion vertex operator algebras, J. Algebra, 2011, 328, 420–431 http://dx.doi.org/10.1016/j.jalgebra.2010.10.015
  • [11] Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206 http://dx.doi.org/10.1007/978-1-4613-9550-8_9
  • [12] Frenkel E., Kac V., Wakimoto M., Characters and fusion rules for W-algebras via quantized Drinfel’d-Sokolov reduction, Comm. Math. Phys., 1992, 147(2), 295–328 http://dx.doi.org/10.1007/BF02096589
  • [13] Frenkel I.B., Huang Y.-Z., Lepowsky J., On Axiomatic Approaches to Vertex Operator Algebras and Modules, Mem. Amer. Math. Soc., 104(494), American Mathematical Society, Providence, 1993
  • [14] Iohara K., Koga Y., Representation Theory of the Virasoro Algebra, Springer Monogr. Math., Springer, London, 2011 http://dx.doi.org/10.1007/978-0-85729-160-8
  • [15] Kac V.G., Wakimoto M., Modular and conformal invariance constraints in representation theory of affine algebras, Adv. in Math., 1988, 70(2), 156–236 http://dx.doi.org/10.1016/0001-8708(88)90055-2
  • [16] Kitazume M., Miyamoto M., Yamada H., Ternary codes and vertex operator algebras, J. Algebra, 2000, 223(2), 379–395 http://dx.doi.org/10.1006/jabr.1999.8058
  • [17] Li H.-S., Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules, In: Moonshine, the Monster, and Related Topics, South Hadley, June 18–23, 1994, Contemp. Math., 193, American Mathematical Society, Providence, 1996, 203–236 http://dx.doi.org/10.1090/conm/193/02373
  • [18] Mauriello C., Branching rule decomposition of irreducible level-1 E 6(1)-modules with respect to the affine subalgebra F 4(1), PhD thesis, State University of New York at Binghamton, 2012 (in preparation)
  • [19] Milas A., Modular forms and almost linear dependence of graded dimensions, In: Lie Algebras, Vertex Operator Algebras and their Applications, Raleigh, May 17–21, 2005, Contemp. Math., 442, American Mathematical Society, Providence, 2007, 411–424 http://dx.doi.org/10.1090/conm/442/08539
  • [20] Miyamoto M., 3-state Potts model and automorphisms of vertex operator algebras of order 3, J. Algebra, 2001, 239(1), 56–76 http://dx.doi.org/10.1006/jabr.2000.8680
  • [21] Mukhin E., Factorization of alternating sums of Virasoro characters, J. Combin. Theory Ser. A, 2007, 114(7), 1165–1181 http://dx.doi.org/10.1016/j.jcta.2006.12.002
  • [22] Wang W., Rationality of Virasoro vertex operator algebras, Internat. Math. Res. Notices, 1993, 7, 197–211 http://dx.doi.org/10.1155/S1073792893000212
  • [23] Xie C.F., Structure of the level two standard modules for the affine Lie algebra A 2(2), Comm. Algebra, 1990, 18(8), 2397–2401 http://dx.doi.org/10.1080/00927879008824029
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0086-7
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