Macdonald Theory and Beyond

Author:   Daniel Orr ,  Joshua Jeishing Wen
Publisher:   American Mathematical Society
ISBN:  

9781470471897


Pages:   159
Publication Date:   30 June 2025
Format:   Paperback
Availability:   In Print   Availability explained
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Macdonald Theory and Beyond


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Overview

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.

Full Product Details

Author:   Daniel Orr ,  Joshua Jeishing Wen
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470471897


ISBN 10:   1470471892
Pages:   159
Publication Date:   30 June 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of 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

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Daniel Orr, Virginia Tech, Blacksburg, VA. Joshua Jeishing Wen, Northeastern University, Boston, MA.

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