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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.
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.
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
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 140 |
| Reihe: | SpringerBriefs in Mathematical Physics |
| Inhalt: |
viii
132 S. 3 s/w Illustr. 132 p. 3 illus. |
| ISBN-13: | 9789819945863 |
| ISBN-10: | 9819945860 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Noumi, Masatoshi |
| Auflage: | 1st ed. 2023 |
| Hersteller: |
Springer Singapore
Springer Nature Singapore SpringerBriefs in Mathematical Physics |
| Maße: | 235 x 155 x 8 mm |
| Von/Mit: | Masatoshi Noumi |
| Erscheinungsdatum: | 09.09.2023 |
| Gewicht: | 0,224 kg |
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
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 140 |
| Reihe: | SpringerBriefs in Mathematical Physics |
| Inhalt: |
viii
132 S. 3 s/w Illustr. 132 p. 3 illus. |
| ISBN-13: | 9789819945863 |
| ISBN-10: | 9819945860 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Noumi, Masatoshi |
| Auflage: | 1st ed. 2023 |
| Hersteller: |
Springer Singapore
Springer Nature Singapore SpringerBriefs in Mathematical Physics |
| Maße: | 235 x 155 x 8 mm |
| Von/Mit: | Masatoshi Noumi |
| Erscheinungsdatum: | 09.09.2023 |
| Gewicht: | 0,224 kg |
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