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Arithmetical investigations : representation theory, orthogonal polynomials, and quantum interpolations / / Shai M.J. Haran



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Autore: Haran Shai M. J Visualizza persona
Titolo: Arithmetical investigations : representation theory, orthogonal polynomials, and quantum interpolations / / Shai M.J. Haran Visualizza cluster
Pubblicazione: Berlin, : Springer, c2008
Edizione: 1st ed. 2008.
Descrizione fisica: xii, 217 p. : ill
Disciplina: 511.42
Soggetto topico: p-adic numbers
Number theory
Interpolation
Representations of quantum groups
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references (p. [209]-213) and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Arithmetical investigations  Visualizza cluster
ISBN: 3-540-78379-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910483366103321
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Serie: Lecture notes in mathematics (Springer-Verlag) ; ; 1941.