Arithmetical investigations [electronic resource] : representation theory, orthogonal polynomials, and quantum interpolations / Shai M.J. Haran.
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 corr...
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Full Text (via Springer) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin :
Springer,
©2008.
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1941. |
| Subjects: |
| 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. |
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| Physical Description: | 1 online resource (xii, 217 pages) : illustrations. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9783540783794 3540783792 3540783784 9783540783787 |
| ISSN: | 0075-8434 ; |
| Source of Description, Etc. Note: | Print version record. |