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Selecta Mathematica

, Volume 23, Issue 4, pp 2397–2436 | Cite as

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

  • Slaven KožićEmail author
Article

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.

Keywords

Affine Lie algebra Quantum affine algebra Quantum vertex algebra Principal subspace Quasi-particle Combinatorial basis Rogers–Ramanujan identities 

Mathematics Subject Classification

17B37 17B69 

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Notes

Acknowledgements

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

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and Statistics F07University of SydneySydneyAustralia
  2. 2.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia

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