Description 
1 online resource (xii, 217 pages) : illustrations 
Series 
Lecture notes in mathematics, 00758434 ; 1941 

Lecture notes in mathematics (SpringerVerlag) ; 1941

Contents 
Introduction: Motivations from Geometry  Gamma and Beta Measures  Markov Chains  Real Beta Chain and qInterpolation  Ladder Structure  qInterpolation of Local Tate Thesis  Pure Basis and SemiGroup  Higher Dimensional Theory  Real Grassmann Manifold  pAdic Grassmann Manifold  qGrassmann Manifold  Quantum Group Uq(su(1, 1)) and the qHahn Basis 
Summary 
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the padic numbers. The padic numbers contain the padic 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 padic 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 "qanalogue" Markov chain, and a special basis, that within certain limits yield the real and the padic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the padic 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 padic Fourier transform and between the real and padic (local unramified part of) Tate thesis, and Weil explicit sums 
Bibliography 
Includes bibliographical references and index 
Notes 
English 

Print version record 
Subject 
Interpolation.


padic numbers.


Representations of quantum groups.

Form 
Electronic book

LC no. 
2008921367 
ISBN 
3540783792 

3540783784 (paperback; alk. paper) 

6611850643 

9783540783794 

9783540783787 (paperback; alk. paper) 

9786611850647 
