Masatoshi Noumi: Macdonald Polynomials

Cover: 9789819945863 | Macdonald Polynomials | Masatoshi Noumi | Taschenbuch | viii | 2023

Dekorationsartikel gehören nicht zum Leistungsumfang.

Sprache: Englisch

43,75 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 2-4 Werktage

Kategorien:

Der Artikel ist nicht in deutscher Sprache verfasst.
Die Sprache der Produktbeschreibung und Details kann in Englisch angegeben sein. Sollten Sie Verständnisprobleme haben, wenden Sie sich gerne an uns.

Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

Overview of Macdonald polynomials.- Preliminaries on symmetric functions.- Schur functions.- Macdonald polynomials: Definition and examples.- Orthogonality and higher order q-di¿erence operators.- Self-duality, Pieri formula and Cauchy formulas.- Littlewood-Richardson coefficients and branching coefficients.- Affine Hecke algebra and q-Dunkl operators (overview).

Erscheinungsjahr:	2023
Fachbereich:	Theoretische Physik
Genre:	Importe , Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	viii 132 S. 3 s/w Illustr. 132 p. 3 illus.
ISBN-13:	9789819945863
ISBN-10:	9819945860
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Noumi, Masatoshi
Auflage:	1st edition 2023
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 8 mm
Von/Mit:	Masatoshi Noumi
Erscheinungsdatum:	09.09.2023
Gewicht:	0,224 kg

Ähnliche Produkte