Overview
- Provides an introduction to Macdonald polynomials requiring only an undergraduate knowledge of algebra and analysis
- Presents selected topics that are easily accessible to readers with a background in mathematical physics
- Gives direct proofs to important theorems and formulas whose proofs are missing or hard to find in the literature
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 50)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the GLn version) as eigenfunctions of a q-difference operator, called the Macdonald–Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting q-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and q-Dunkl operators.
Authors and Affiliations
About the author
The author is currently Professor Emeritus at Kobe University and Professor at Rikkyo University. He previously held positions at Sophia University and the University of Tokyo. He was Invited Speaker at the ICM 2002 and also Plenary Speaker at the ICMP 2018.
Bibliographic Information
Book Title: Macdonald Polynomials
Book Subtitle: Commuting Family of q-Difference Operators and Their Joint Eigenfunctions
Authors: Masatoshi Noumi
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-99-4587-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Softcover ISBN: 978-981-99-4586-3Published: 09 September 2023
eBook ISBN: 978-981-99-4587-0Published: 08 September 2023
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: VIII, 132
Number of Illustrations: 3 b/w illustrations
Topics: Mathematical Physics, Special Functions, Associative Rings and Algebras