Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915450998226944 |
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| author | Primc, Mirko Trupčević, Goran |
| author_facet | Primc, Mirko Trupčević, Goran |
| contents | In the previous paper, the authors proved linear independence of the combinatorial spanning set for standard $C_\ell^{(1)}$-module $L(kΛ_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace $W(kΛ_0)$ of $C_{2\ell}^{(1)}$-module $L(kΛ_0)$. In this note we extend this argument for $C_{1}^{(1)}\cong A_{1}^{(1)}$ to all standard $A_{1}^{(1)}$-modules $L(Λ)$. In the proof we use a coefficient of an intertwining operator of the type $\binom{L(Λ_2)}{L(Λ_1)\ L(Λ_1)}$ for standard $C_{2}^{(1)}$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$ Primc, Mirko Trupčević, Goran Quantum Algebra 17B67, 17B69 In the previous paper, the authors proved linear independence of the combinatorial spanning set for standard $C_\ell^{(1)}$-module $L(kΛ_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace $W(kΛ_0)$ of $C_{2\ell}^{(1)}$-module $L(kΛ_0)$. In this note we extend this argument for $C_{1}^{(1)}\cong A_{1}^{(1)}$ to all standard $A_{1}^{(1)}$-modules $L(Λ)$. In the proof we use a coefficient of an intertwining operator of the type $\binom{L(Λ_2)}{L(Λ_1)\ L(Λ_1)}$ for standard $C_{2}^{(1)}$-modules. |
| title | Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$ |
| topic | Quantum Algebra 17B67, 17B69 |
| url | https://arxiv.org/abs/2504.15597 |