Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations

Shai M. J. Haran

ISBN 10: 3540783784 / ISBN 13: 9783540783787

Edité par Springer, Springer Vieweg, 2008

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9783540783787

Détails bibliographiques

• Titre: Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
• Éditeur: Springer, Springer Vieweg
• Date de parution: 2008
• Langue: anglais
• ISBN à 10 chiffres: 3540783784
• ISBN à 13 chiffres: 9783540783787
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 13 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 13 millimètres de profondeur
• Poids: 365 grammes

A propos de ce titre

Synopsis

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 Z_p which are the inverse limit of the finite rings Z/pⁿ. This gives rise to a tree, and probability measures w on Z_p correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L₂(Z_p,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 GL_n(q)that interpolates between the p-adic group GL_n(Z_p), and between its real (and complex) analogue -the orthogonal O_n (and unitary U_n )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.

Présentation de l'éditeur

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.