Geodesic
A raising operator formula for Macdonald polynomials
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e47

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\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. 
Blasiak, J.; Haiman, M.; Morse, J.; Pun, A.; Seelinger, G. H. A raising operator formula for Macdonald polynomials. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e47. doi: 10.1017/fms.2025.8
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