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Theta operators at $t=1$, Macdonald cumulants, and LLT positivity
We study the Theta operators of D'Adderio-Iraci-Vanden Wyngaerd at $t=1$ and show that the power-sum-indexed operators $Θ_{\mathsf p_k}|_{t=1}$ agree with a commuting family of derivations when restricted to symmetric functions of positive degree. Writing $\widetilde{h}_a$ for the modified Macdonald
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