| Description |
1 online resource (xii, 217 pages) : illustrations |
| Series |
Lecture notes in mathematics, 0075-8434 ; 1941 |
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Lecture notes in mathematics (Springer-Verlag) ; 1941.
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| Contents |
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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Interpolation.
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p-adic numbers.
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Representations of quantum groups.
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p-adic numbers.
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Representations of quantum groups.
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Interpolation.
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Interpolation
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p-adic numbers
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Representations of quantum groups
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| Form |
Electronic book
|
| ISBN |
9783540783794 |
|
3540783792 |
|
3540783784 |
|
9783540783787 |
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9786611850647 |
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6611850643 |
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9781281850645 |
|
1281850640 |
|
