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Macdonald Polynomials

Commuting Family of q-Difference Operators and Their Joint Eigenfunctions de

Éditeur :

Springer


Collection :

SpringerBriefs in Mathematical Physics

Paru le : 2023-09-08

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Description


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.
Pages
132 pages
Collection
SpringerBriefs in Mathematical Physics
Parution
2023-09-08
Marque
Springer
EAN papier
9789819945863
EAN PDF
9789819945870
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
1577 Ko
Prix
47,46 €
EAN EPUB
9789819945870
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
13
Taille du fichier
12943 Ko
Prix
47,46 €

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