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Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$

O. Foda·K. Iohara·M. Jimbo·R. Kedem·T. Miwa·H. Yan
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Abstract

We discuss a construction of highest weight modules for the recently defined elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures concerning them. The modules are generated by the action of the components of the operator $L$ on the highest weight vectors. We introduce the vertex operators $Φ$ and $Ψ^*$ through their commutation relations with the $L$-operator. We present ordering rules for the $L$- and $Φ$-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of $\widehat{sl}_2$-modules.

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O. Foda, K. Iohara, M. Jimbo, R. Kedem, T. Miwa, H. Yan. 1994-05-10. Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$. https://doi.org/10.1143/ptps.118.1

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