Macdonald Polynomials

Commuting Family of q-Difference Operators and Their Joint Eigenfunctions

Masatoshi Noumi (Autor)

Buch | Softcover

132 Seiten

2023 | 1st ed. 2023
Springer Verlag, Singapore
978-981-99-4586-3 (ISBN)

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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.

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.

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).

Erscheinungsdatum	13.09.2023
Reihe/Serie	SpringerBriefs in Mathematical Physics
Zusatzinfo	3 Illustrations, black and white; VIII, 132 p. 3 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Macdonald polynomial • q-difference equation • q-orthogonal polynomial • quantum integrable system • Symmetric functions
ISBN-10	981-99-4586-0 / 9819945860
ISBN-13	978-981-99-4586-3 / 9789819945863
Zustand	Neuware