Twisted and non-twisted deformed Virasoro algebras via vertex operators of \(U_q(\widehat{\mathfrak {sl}}_2)\)


The work is devoted to a probably new connection between deformed Virasoro algebra and quantum affine algebra \(\mathfrak {sl}_2\). We give an explicit realization of Virasoro current via the vertex operators of the level 1 integrable representations of quantum affine algebra \(\mathfrak {sl}_2\). The same is done for a twisted version of deformed Virasoro algebra.

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We are grateful to B. Feigin, E. Gorsky, M. Jimbo, M. Lashkevich, A. Neguț, Y. Pugai, J. Shiraishi for interest in our work and discussions. The work was partially supported by the Russian Foundation of Basic Research under grant mol_a_ved 18-31-20062 and by the HSE University Basic Research Program, Russian Academic Excellence Project ’5-100. R.G. was also supported by the ‘Young Russian Mathematics’ award.

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Correspondence to Mikhail Bershtein.

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Bershtein, M., Gonin, R. Twisted and non-twisted deformed Virasoro algebras via vertex operators of \(U_q(\widehat{\mathfrak {sl}}_2)\). Lett Math Phys 111, 22 (2021).

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  • Deformed Virasoro algebra
  • Quantum affine algebra
  • Vertex operators

Mathematics Subject Classification

  • 17B68
  • 17B37
  • 17B69
  • 17B67
  • 81R10