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- W4384389905 abstract "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." @default.
- W4384389905 created "2023-07-15" @default.
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- W4384389905 date "2023-07-12" @default.
- W4384389905 modified "2023-09-26" @default.
- W4384389905 title "A raising operator formula for Macdonald polynomials" @default.
- W4384389905 doi "https://doi.org/10.48550/arxiv.2307.06517" @default.
- W4384389905 hasPublicationYear "2023" @default.
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