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A basis of the basic $germ sgerm l(3,Bbb C)sp sim$-module.

Meurman, Arne LU and Primc, Mirko (2001) In Communications in Contemporary Mathematics 3(No. 4). p.593-614
Abstract
J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In this approach the first new combinatorial identities were discovered by S. Capparelli through the construction of the level 3 standard $A_2^{(2)}$-modules. We obtained several infinite series of new combinatorial identities through the construction of all standard $A_1^{(1)}$-modules; the identities associated to the fundamental modules coincide with the two Capparelli identities. In this paper we extend our construction to the basic $A_2^{(1)}$-module and, by using the principal specialization of the Weyl-Kac character formula, we obtain a Rogers-Ramanujan... (More)
J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In this approach the first new combinatorial identities were discovered by S. Capparelli through the construction of the level 3 standard $A_2^{(2)}$-modules. We obtained several infinite series of new combinatorial identities through the construction of all standard $A_1^{(1)}$-modules; the identities associated to the fundamental modules coincide with the two Capparelli identities. In this paper we extend our construction to the basic $A_2^{(1)}$-module and, by using the principal specialization of the Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorial identity for colored partitions. The new combinatorial identity indicates the next level of complexity which one should expect in Lepowsky-Wilson's approach for affine Lie algebras of higher ranks, say for $A_n^{(1)}, $nge 2$, in a way parallel to the next level of complexity seen when passing from the Rogers-Ramanujan identities (for modulus 5) to the Gordon identities for odd moduli $ge 7$. (Less)
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organization
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Contribution to journal
publication status
published
subject
keywords
partition ideals., colored partitions, Rogers-Ramanujan identities, standard modules, vertex operator formula, vertex operator algebras, Affine Lie algebras
in
Communications in Contemporary Mathematics
volume
3
issue
No. 4
pages
593 - 614
publisher
World Scientific
language
English
LU publication?
yes
id
2a5e8968-ea37-454c-892c-01131c40943b (old id 627401)
date added to LUP
2007-12-10 10:18:47
date last changed
2017-03-13 14:27:21
@article{2a5e8968-ea37-454c-892c-01131c40943b,
  abstract     = {J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In this approach the first new combinatorial identities were discovered by S. Capparelli through the construction of the level 3 standard $A_2^{(2)}$-modules. We obtained several infinite series of new combinatorial identities through the construction of all standard $A_1^{(1)}$-modules; the identities associated to the fundamental modules coincide with the two Capparelli identities. In this paper we extend our construction to the basic $A_2^{(1)}$-module and, by using the principal specialization of the Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorial identity for colored partitions. The new combinatorial identity indicates the next level of complexity which one should expect in Lepowsky-Wilson's approach for affine Lie algebras of higher ranks, say for $A_n^{(1)}, $nge 2$, in a way parallel to the next level of complexity seen when passing from the Rogers-Ramanujan identities (for modulus 5) to the Gordon identities for odd moduli $ge 7$.},
  author       = {Meurman, Arne and Primc, Mirko},
  keyword      = {partition ideals.,colored partitions,Rogers-Ramanujan identities,standard modules,vertex operator formula,vertex operator algebras,Affine Lie algebras},
  language     = {eng},
  number       = {No. 4},
  pages        = {593--614},
  publisher    = {World Scientific},
  series       = {Communications in Contemporary Mathematics},
  title        = {A basis of the basic $germ sgerm l(3,Bbb C)sp sim$-module.},
  volume       = {3},
  year         = {2001},
}