Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$

Mirko Primc; Goran Trupčević

doi:10.3842/sigma.2025.071

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arXiv · 2504.15597

Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$

Mirko Primc·Goran Trupčević

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Abstract

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.

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BibTeX RIS

Mirko Primc, Goran Trupčević. 2025-08-19. Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$. https://doi.org/10.3842/sigma.2025.071

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