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" Arithmetical investigations : "
Shai M.J. Haran.
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BL
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| Record Number
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981861
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b736231
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| Main Entry
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Haran, M. J. Shai.
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| Title & Author
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Arithmetical investigations : : representation theory, orthogonal polynomials, and quantum interpolations /\ Shai M.J. Haran.
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| Publication Statement
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Berlin :: Springer,, ©2008.
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| Series Statement
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Lecture notes in mathematics,; 1941
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| Page. NO
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1 online resource (xii, 217 pages) :: illustrations
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| ISBN
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3540783784
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: 3540783792
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: 6611850643
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: 9783540783787
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: 9783540783794
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: 9786611850647
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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.
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| Abstract
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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.
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Interpolation.
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p-adic numbers.
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Representations of quantum groups.
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Interpolation.
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p-adic numbers.
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Representations of quantum groups.
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Interpolation.
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p-adic numbers.
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Representations of quantum groups.
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| Dewey Classification
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511.42
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| LC Classification
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QA3.L28 no. 1941
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| NLM classification
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O174. 41clc
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