汇报标题 (Title)：The modified Macdonald polynomials and mu-Mahonian statistics（优化的Macdonald多项式和mu-Mahonian统计量）
汇报人 (Speaker)：靳宇 教授（乐山大学）
汇报功夫 (Time)：2025年11月6日（周四）15:00—16:00
汇报地址：腾讯会议：535-192-205
约请人(Inviter)：王晓霞 教授
主办部门：理学院数学系
汇报提要：The modified Macdonald polynomials indexed by partitions are the basis of the symmetric functions in infinitely many variables with coefficients in the field of rational functions of two variables. The combinatorial investigation of modified Macdonald polynomials has been greatly promoted by the celebrated breakthrough on the connections between them and mu-Mahonian statistics on fillings of Young diagrams due to Haglund, Haiman and Loehr (2005).
Recently, Corteel, Haglund, Mandelshtam, Mason and Williams (2021) discovered a compact formula for the modified Macdonald polynomials and made a conjecture on an equivalent form of them. This was subsequently affirmed by Ayyer, Mandelshtam and Martin (2023) and they proposed a stronger conjecture on a refined equivalence. Our main result confirms their conjecture. That is, we establish the equidistribution between the pairs (inv, maj) and (quinv, maj) on any row-equivalency class of a given filling of a Young diagram. In particular if the Young diagram is rectangular, the triples (inv, quinv, maj) and (quinv, inv, maj) have the same distribution over the row-equivalence class. This talk is based on joint work with Xiaowei Lin.
