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Lepowsky's and Wakimoto's product formulas for the affine Lie algebras Cl(1)

Butorac, M. ; Kožić, S. ; Meurman, A. LU and Primc, M. (2024) In Journal of Algebra 660. p.147-189
Abstract

In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type Cl(1), Dl+1(2) and A2l(2). Lepowsky–Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers–Ramanujan-type combinatorial identities for affine Lie algebras of type Cl(1).

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Character formulas, Representations of affine Lie algebras, Rogers-Ramanujan-type identities
in
Journal of Algebra
volume
660
pages
43 pages
publisher
Academic Press
external identifiers
  • scopus:85199940266
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2024.06.040
language
English
LU publication?
yes
id
81544967-9454-4748-baef-a72fc893f5c1
date added to LUP
2024-08-26 13:40:42
date last changed
2025-04-04 14:56:18
@article{81544967-9454-4748-baef-a72fc893f5c1,
  abstract     = {{<p>In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type C<sub>l</sub><sup>(1)</sup>, D<sub>l+1</sub><sup>(2)</sup> and A<sub>2l</sub><sup>(2)</sup>. Lepowsky–Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers–Ramanujan-type combinatorial identities for affine Lie algebras of type C<sub>l</sub><sup>(1)</sup>.</p>}},
  author       = {{Butorac, M. and Kožić, S. and Meurman, A. and Primc, M.}},
  issn         = {{0021-8693}},
  keywords     = {{Character formulas; Representations of affine Lie algebras; Rogers-Ramanujan-type identities}},
  language     = {{eng}},
  pages        = {{147--189}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Algebra}},
  title        = {{Lepowsky's and Wakimoto's product formulas for the affine Lie algebras C<sub>l</sub><sup>(1)</sup>}},
  url          = {{http://dx.doi.org/10.1016/j.jalgebra.2024.06.040}},
  doi          = {{10.1016/j.jalgebra.2024.06.040}},
  volume       = {{660}},
  year         = {{2024}},
}