## Explicit generators in rectangular affine $$\mathcal{W}$$-algebras of type $$A$$

### Tomoyuki Arakawa and Alexander Molev

#### Abstract

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.

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 Monday, March 10, 2014