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Higher level vertex operators for \(U_q \left( \widehat{\mathfrak {sl}}_2\right) \)

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Abstract

We study graded nonlocal \(\underline{\mathsf {q}}\)-vertex algebras and we prove that they can be generated by certain sets of vertex operators. As an application, we consider the family of graded nonlocal \(\underline{\mathsf {q}}\)-vertex algebras \(V_{c,1}\), \(c\ge 1\), associated with the principal subspaces \(W(c\Lambda _0)\) of the integrable highest weight \(U_q (\widehat{\mathfrak {sl}}_2)\)-modules \(L(c\Lambda _0)\). Using quantum integrability, we derive combinatorial bases for \(V_{c,1}\) and compute the corresponding character formulae.

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Acknowledgements

The author would like to thank Mirko Primc for his valuable comments on the earlier version of the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW, 2006, Australia

    Slaven Kožić

  2. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Slaven Kožić

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  1. Slaven Kožić
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Correspondence to Slaven Kožić.

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The research was supported by the Australian Research Council and partially supported by the Croatian Science Foundation under the Project 2634.

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Kožić, S. Higher level vertex operators for \(U_q \left( \widehat{\mathfrak {sl}}_2\right) \) . Sel. Math. New Ser. 23, 2397–2436 (2017). https://doi.org/10.1007/s00029-017-0348-0

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