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.

---

Date published: Wednesday, February 22, 2023