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Preprint
A raising operator formula for Macdonald polynomials
arXiv.org
12 Jul 2023
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.
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Details
- Title
- A raising operator formula for Macdonald polynomials
- Creators
- Jonah BlasiakMark HaimanJennifer MorseAnna PunGeorge Seelinger
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862388004721