Arithmetical Investigations : Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
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...
Enregistré dans:
| Auteur principal: | |
|---|---|
| Autres auteurs: | |
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2008. |
| Collection: | Lecture Notes in Mathematics
1941 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
L'impression du document génère 223 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Arithmetical investigations, representation theory, orthogonal polynomials, and quantum interpolations, Shai M.J. Haran, Berlin, Springer, 2008, 1 vol. (XII-217 p.), Lecture notes in mathematics, 978-3-540-78378-7 • Arithmetical Investigations, Texte imprimé, 9783540849216 • Arithmetical investigations, representation theory, orthogonal polynomials, and quantum interpolations, Shai M.J. Haran, Berlin, Springer, 2008, 1 vol. (XII-217 p.), Lecture notes in mathematics, 978-3-540-78378-7 |
| LEADER | 04507nam a22005417a 4500 | ||
|---|---|---|---|
| 001 | 940421 | ||
| 008 | 080626q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN125218338 | ||
| 020 | |a 9783540783794 | ||
| 041 | 0 | |a eng | |
| 082 | |a 511.42 | ||
| 082 | |a 510 | ||
| 084 | |a 11M36. 2010 | ||
| 084 | |a 11S80. 2010 | ||
| 084 | |a 11S85. 2010 | ||
| 084 | |a 11M. 2010 | ||
| 084 | |a 60J10. 2010 | ||
| 100 | 1 | |a Haran, Shai M J. | |
| 245 | 1 | 0 | |a Arithmetical Investigations : |b Representation Theory, Orthogonal Polynomials, and Quantum Interpolations |c Shai M. J. Haran. |
| 250 | |a 1st ed. 2008. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture Notes in Mathematics |v 1941 |x 1617-9692 | |
| 500 | |a L'impression du document génère 223 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 650 | |a Interpolation (mathématiques) | ||
| 650 | |a Nombres p-adiques | ||
| 650 | |a Groupes quantiques | ||
| 650 | |a Markov, processus de | ||
| 650 | |a Variétés de Grassmann | ||
| 650 | |a Mathématiques | ||
| 650 | |a Nombres, Théorie des | ||
| 700 | 1 | |a Haran, Shai Moshe Joseph, |d 1958- |4 edt | |
| 776 | 0 | |0 124141684 |t Arithmetical investigations |o representation theory, orthogonal polynomials, and quantum interpolations |f Shai M.J. Haran |c Berlin |n Springer |d 2008 |p 1 vol. (XII-217 p.) |s Lecture notes in mathematics |z 978-3-540-78378-7 | |
| 776 | 0 | |t Arithmetical Investigations |b Texte imprimé |z 9783540849216 | |
| 776 | 0 | |0 124141684 |t Arithmetical investigations |o representation theory, orthogonal polynomials, and quantum interpolations |f Shai M.J. Haran |c Berlin |n Springer |d 2008 |p 1 vol. (XII-217 p.) |s Lecture notes in mathematics |z 978-3-540-78378-7 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-540-78379-4 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-0WJ740M2-P |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747860866 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-3-540-78379-4 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750878398 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-3-540-78379-4 |z Accès INSA CVL | |
| 997 | |0 940421 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||