Linear independence for $C_\ell^{(1)}$ by using $C_{2\ell}^{(1)}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909286407340032 |
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| author | Primc, Mirko Trupčević, Goran |
| author_facet | Primc, Mirko Trupčević, Goran |
| contents | In this note we prove 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 $L(kΛ_0)$. It should be noted that the proof of linear independence for the basis of $W(kΛ_0)$ is obtained by using simple currents and intertwining operators in the vertex operator algebra $L(kΛ_0)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear independence for $C_\ell^{(1)}$ by using $C_{2\ell}^{(1)}$ Primc, Mirko Trupčević, Goran Quantum Algebra 17B67 (Primary), 17B69 (Secondary) In this note we prove 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 $L(kΛ_0)$. It should be noted that the proof of linear independence for the basis of $W(kΛ_0)$ is obtained by using simple currents and intertwining operators in the vertex operator algebra $L(kΛ_0)$. |
| title | Linear independence for $C_\ell^{(1)}$ by using $C_{2\ell}^{(1)}$ |
| topic | Quantum Algebra 17B67 (Primary), 17B69 (Secondary) |
| url | https://arxiv.org/abs/2403.06881 |