Arithmetical Investigations [[electronic resource] ] : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations / / by Shai M. J. Haran

• Autore: Haran Shai M. J
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2008
• Edizione: 1st ed. 2008.
• Descrizione fisica: xii, 217 p. : ill
• Disciplina: 511.42
• Soggetto topico: Number theory; Number Theory
• 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
• ISBN: 3-540-78379-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466535803316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434