Super duality for Whittaker modules and finite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -algebras

We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev–Shu–Xiao decomposition, we obtain a super duality which is an equivalence between module categories over a pair of finite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -algebras and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -superalgebras at the infinite-rank limit.