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Title:聽Delta and Theta Operator expansions in the theory of Macdonald polynomials

础产蝉迟谤补肠迟:听Delta and Theta operators are fundamental in the theory of modified Macdonald polynomials. Theta operators were recently used to give and prove the compositional version of the Delta Conjecture; and they also conjecturally give a symmetric function description for the $S_n$ coinvariants in the polynomial ring with two commuting and two anti-commuting sets of variables. We will start by introducing some of these important conjectures and theorems.

We will then give a new combinatorial model for describing general applications of Delta and Theta operators when $t=1$ in terms of what we call $gamma$-Parking Functions. We will end by highlighting a few of the important methods used in proving this result, one of which is an application of the combinatorial formula for the forgotten symmetric functions.