Theta operators at $t=1$, Macdonald cumulants, and LLT positivity

Jim Haglund, Vasu Tewari

We study the Theta operators of D'Adderio-Iraci-Vanden Wyngaerd at $t=1$ and show that the power-sum-indexed operators ${\Theta }_{{\mathsf{p}}_k}{|}_{t=1}$ agree with a commuting family of der…