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Macdonald Polynomials : Commuting Family of Q-Difference Operators and Their Joint Eigenfunctions by Masatoshi Noumi is a nonfiction available to read on EtoBox.

What is Macdonald Polynomials : Commuting Family of Q-Difference Operators and Their Joint Eigenfunctions about?

This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021. 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.

Who reads Macdonald Polynomials : Commuting Family of Q-Difference Operators and Their Joint Eigenfunctions?

Author

Masatoshi Noumi

Publisher

Springer Nature Singapore Pte Ltd Fka Springer Science + Business Media Singapore Pte Ltd

Published

2023

Language

EN

ISBN

9789819945863

Category

nonfiction

Subjects

Mathematics, Science, Physics