Arithmetical Investigations Representation Theory, Orthogonal Polynomials, and Quantum Interpolations /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Haran, Shai M. J. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Mathematics, 1941
• Subjects: Mathematics.; Number theory.; Number Theory.

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...

Table of Contents:

• 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.