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Full Description
This volume contains the proceedings of the AMS Special Session on Macdonald Theory and Beyond: Combinatorics, Geometry, and Integrable Systems, held virtually on March 19-20, 2022. The articles in this volume represent a number of recent developments in the theory of Macdonald polynomials while highlighting some of its many connections to other areas of mathematics. An important common thread throughout the volume is the role of combinatorial formulas-for Macdonald polynomials themselves as well as operations on them arising from rich additional structures. The articles of Haglund, Mandelshtam, and Romero concern the type A Macdonald polynomials, which remain a major focus of the subject due to the depth of their combinatorial theory and the power of their specific applications. For arbitrary type Macdonald polynomials, a new combinatorial formula with pseudo-crystal structure is presented in the article of Lenart, Naito, Nomoto, and Sagaki. Finally, the articles of Saied and Wen take up two important new directions in the subject: the SSV polynomials arising from the study of special functions on metaplectic groups, and the wreath Macdonald polynomials associated with certain symplectic resolutions.
Contents
Articles
J. Haglund, Combinatorial formulas for (type A) Macdonald polynomials
Cristian Lenart, Satoshi Naito, Fumihiko Nomoto and Daisuke Sagaki, Symmetric and nonsymmetric Macdonald polynomials via a path model with a pseudo-crystal structure
Joshua Jeishing Wen, Shuffle approach to wreath Pieri operators
Olya Mandelshtam, New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
Marino Romero, Some combinatorial aspects of Theta and Delta operators
Jason Saied, A Littlewood-Richardson rule for SSV polynomials
