Speaker：Ning Liu (South China University of Technology)

Time：2024-1-24, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

In this talk, we will start by the classical Murnaghan-Nakayama rule for the symmetric group. Subsequently, we will review briefly two q- Murnaghan-Nakayama rules for Hecke algebra and Hecke-Clifford algebra. After that, we introduce our main result: a multi-parameter M-N rule for Macdonald polynomials, which will specialize to the two q-M-N rules mentioned above. Fi- nally, we will take account into some applications of our multi-parameter M-N rule to an inversion of the Pieri rule of Hall-Littlewood functions and (q,t)- Kostka polynomials. If time permits, an application to the Petrie functions found recently will also be discussed. This talk is based on the joint work with Naihuan Jing.