A combinatorial skewing formula for the Rise Delta Theorem
We prove that the symmetric function $\Delta'_{e_{k-1}}e_n$ appearing in the Delta Conjecture can be obtained from the symmetric function in the Rational Shuffle Theorem by applying a Schur skewing operator. This generalizes a formula by the first and third authors for the Delta Conjecture at $...
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Zusammenfassung: | We prove that the symmetric function $\Delta'_{e_{k-1}}e_n$ appearing in the
Delta Conjecture can be obtained from the symmetric function in the Rational
Shuffle Theorem by applying a Schur skewing operator. This generalizes a
formula by the first and third authors for the Delta Conjecture at $t=0$, and
follows from work of Blasiak, Haiman, Morse, Pun, and Seelinger.
Our main result is that we also provide a purely combinatorial proof of this
skewing identity, giving a new proof of the Rise Delta Theorem from the
Rational Shuffle Theorem. |
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DOI: | 10.48550/arxiv.2408.12543 |