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 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. INDICE: Introduction: Motivations from Geometry.- Gamma and Beta Measures.- Markov Chains.- Real Beta cchain and q-Interpolation.- Ladder Structure.- q-Interpolation of Local Tate Thesis.- Pure Basis and Semi-group.- Higher Dimentional Theory.- Real Grassmann Manifold.- p-Adic Grasmann Manifold.- q-Grassmann Manifold.- Quantum Group Uq(su1,1) and the q-Hahn Basis.- Problems and Questions.- Orthogonal Polynomials.- Record.- Bibliography.- Index

• ISBN: 978-3-540-78378-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 190
• Fecha Publicación: 01/05/2008
• Nº Volúmenes: 1
• Idioma: Inglés