A proof of the Extended Delta Conjecture

Abstract: We prove the Extended Delta Conjecture of Haglund, Remmel, and Wilson, a combinatorial formula for $\Delta {h_l}\Delta' _{e_k} e{n}$, where $\Delta' {e_k}$ and $\Delta{h_l}$ are Macdonald eigenoperators and $e_n$ is an elementary symmetric function. We actually prove a stronger identity of infinite series of $GL_m$ characters expressed in terms of LLT series. This is achieved through new results in the theory of the Schiffmann algebra and its action on the algebra of symmetric functions.