A raising operator formula for Macdonald polynomials

We give an explicit raising operator formula for the modified Macdonald polynomials ${\tilde{H}}_{\mu }(X;q,t)$, which follows from our recent formula for $\mathrm{\nabla }$ on an LLT polynomial and the Haglund-Haiman-Loehr formula expressing modified Macdonald polynomials as sums of LLT polynomials. Our method just as easily yields a formula for a family of symmetric functions ${\tilde{H}}^{1,n}(X;q,t)$ that we call $1,n$-Macdonald polynomials, which reduce to a scalar multiple of ${\tilde{H}}_{\mu }(X;q,t)$ when $n=1$. We conjecture that the coefficients of $1,n$-Macdonald polynomials in terms of Schur functions belong to $\mathbb{N}[q,t]$, generalizing Macdonald positivity.