The nabla operator, Hall--Littlewood polynomials and LLT polynomials

Feng Gu, Mingyang Kang, Dun Qiu +1

Bergeron, Garsia, Haiman, and Tesler conjectured that $(-1{)}^{n-\ell (\mu )}\nabla {\tilde{H}}_{\mu }[X;0,t]$ and $\nabla \omega {\tilde{H}}_{\mu }[X;0,t^{-1}]$ are Schur positive, and that $\nablaω\wi…