A combinatorial skewing formula for the Rise Delta Theorem (2408.12543v1)

Abstract: 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.