Band 50
Macdonald Polynomials Commuting Family of q-Difference Operators and Their Joint Eigenfunctions
Aus der Reihe
SpringerBriefs in Mathematical Physics
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Form:Einzelkauf Download
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Sprache:Englisch
Fr. 62.90
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Produktdetails
Format
Kopierschutz
Nein
Family Sharing
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Erscheinungsdatum
08.09.2023
Verlag
Springer Nature SingaporeSeitenzahl
132 (Printausgabe)
Dateigröße
1581 KB
Auflage
1st ed. 2023
Sprache
Englisch
EAN
9789819945870
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 GL
n 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.
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