| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910483366103321 |
|
|
Autore |
Haran Shai M. J |
|
|
Titolo |
Arithmetical investigations : representation theory, orthogonal polynomials, and quantum interpolations / / Shai M.J. Haran |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, : Springer, c2008 |
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
|
|
Edizione |
[1st ed. 2008.] |
|
|
|
|
|
Descrizione fisica |
|
|
|
|
|
|
Collana |
|
Lecture notes in mathematics, , 0075-8434 ; ; 1941 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
p-adic numbers |
Number theory |
Interpolation |
Representations of quantum groups |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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. |
|
|
|
|
|
| |