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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Notes
It is easy to verify that \({\text {cdet}}B\) coincides with the row-determinant of B defined in a similar way.
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Arakawa, T., Molev, A. Explicit generators in rectangular affine \(\mathcal {W}\)-algebras of type A . Lett Math Phys 107, 47–59 (2017). https://doi.org/10.1007/s11005-016-0890-2
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DOI: https://doi.org/10.1007/s11005-016-0890-2