Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations / edited by Shai M. J. Haran
(Lecture Notes in Mathematics ; 1941)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg |
| 出版年 | 2008 |
| 本文言語 | 英語 |
| 大きさ | online resource |
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| 内容注記 | 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 |
|---|---|
| 一般注記 | 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 |
| 著者標目 | Haran, Shai M. J. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Number theory FREE:Mathematics FREE:Number Theory |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9783540783794 
|
| ISBN | 9783540783794 |
| URL | http://dx.doi.org/10.1007/978-3-540-78379-4 |
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