Macdonald Theory and Beyond

Proceedings from a virtual AMS Special Session delve into recent advances in Macdonald polynomials and their intricate combinatorial structures. Discussions span both type A and arbitrary types, unveiling new formulas connected to integrable systems, SSV polynomials, and wreath Macdonald polynomials in symplectic resolutions.
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.

Contributor: Daniel Orr (Edited by), Joshua Jeishing Wen (Edited by)

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