Lepowsky's and Wakimoto's product formulas for the affine Lie algebras $C_l^{(1)}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917737846013952 |
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| author | Butorac, Marijana Kožić, Slaven Meurman, Arne Primc, Mirko |
| author_facet | Butorac, Marijana Kožić, Slaven Meurman, Arne Primc, Mirko |
| contents | 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 $C_l^{(1)}$, $D_{l+1}^{(2)}$ and $A_{2l}^{(2)}$. Lepowsky-Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers-Ramanujan-type combinatorial identities for affine Lie algebras of type $C_l^{(1)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lepowsky's and Wakimoto's product formulas for the affine Lie algebras $C_l^{(1)}$ Butorac, Marijana Kožić, Slaven Meurman, Arne Primc, Mirko Representation Theory Mathematical Physics Combinatorics Quantum Algebra 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 $C_l^{(1)}$, $D_{l+1}^{(2)}$ and $A_{2l}^{(2)}$. Lepowsky-Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers-Ramanujan-type combinatorial identities for affine Lie algebras of type $C_l^{(1)}$. |
| title | Lepowsky's and Wakimoto's product formulas for the affine Lie algebras $C_l^{(1)}$ |
| topic | Representation Theory Mathematical Physics Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2403.05456 |