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Differential Operators for Macdonald's Hypergeometric Functions
Hong Chen
Location: Hill 705
Date & time: Wednesday, 09 April 2025 at 10:45AM - 11:45PM
Date: 04/09/2025
Speaker: Hong Chen (Rutgers)
Title: Differential Operators for Macdonald's Hypergeometric Functions
Abstract: In his widely circulated 1980s manuscript (now available as [arXiv:1309.4568]), Macdonald introduced hypergeometric functions with a parameter alpha (the Jack parameter) and posed foundational questions about their properties. In this talk, I will present a general construction of differential operators pDq that characterize Macdonald’s hypergeometric functions pFq for arbitrary p and q. These operators generalize the ones studied by Constantine--Muirhead, Fujikoshi, and Macdonald.