Letters in Mathematical Physics

, Volume 107, Issue 1, pp 47–59 | Cite as

Explicit generators in rectangular affine \(\mathcal {W}\)-algebras of type A

  • Tomoyuki Arakawa
  • Alexander MolevEmail author


We produce in an explicit form free generators of the affine \(\mathcal {W}\)-algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent case and we thus recover the quantum Miura transformation of Fateev and Lukyanov.


Vertex algebra Affine W-algebra Miura transformation 

Mathematics Subject Classification



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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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