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Cover: 9783540783787 | Arithmetical Investigations | Shai M. J. Haran | Taschenbuch | xii
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Arithmetical Investigations
Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
Taschenbuch von Shai M. J. Haran
Sprache: Englisch

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Beschreibung
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Introduction: Motivations from Geometry.- Gamma and Beta Measures.- Markov Chains.- Real Beta Chain and q-Interpolation.- Ladder Structure.- q-Interpolation of Local Tate Thesis.- Pure Basis and Semi-Group.- Higher Dimensional Theory.- Real Grassmann Manifold.- p-Adic Grassmann Manifold.- q-Grassmann Manifold.- Quantum Group Uq(su(1, 1)) and the q-Hahn Basis.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: xii
222 S.
23 s/w Illustr.
222 p. 23 illus.
ISBN-13: 9783540783787
ISBN-10: 3540783784
Sprache: Englisch
Herstellernummer: 12231904
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Haran, Shai M. J.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 235 x 155 x 13 mm
Von/Mit: Shai M. J. Haran
Erscheinungsdatum: 02.05.2008
Gewicht: 0,365 kg
Artikel-ID: 101850524
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Introduction: Motivations from Geometry.- Gamma and Beta Measures.- Markov Chains.- Real Beta Chain and q-Interpolation.- Ladder Structure.- q-Interpolation of Local Tate Thesis.- Pure Basis and Semi-Group.- Higher Dimensional Theory.- Real Grassmann Manifold.- p-Adic Grassmann Manifold.- q-Grassmann Manifold.- Quantum Group Uq(su(1, 1)) and the q-Hahn Basis.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: xii
222 S.
23 s/w Illustr.
222 p. 23 illus.
ISBN-13: 9783540783787
ISBN-10: 3540783784
Sprache: Englisch
Herstellernummer: 12231904
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Haran, Shai M. J.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 235 x 155 x 13 mm
Von/Mit: Shai M. J. Haran
Erscheinungsdatum: 02.05.2008
Gewicht: 0,365 kg
Artikel-ID: 101850524
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