{"product_id":"9783540783787","title":"Lecture Notes in Mathematics: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations","description":"\u003ch1\u003eLecture Notes in Mathematics: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations\u003c\/h1\u003e \u003ch2\u003eHaran, Shai M. J.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn 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 Z\u003csub\u003ep\u003c\/sub\u003e which are the inverse limit of the finite rings Z\/p\u003csup\u003en\u003c\/sup\u003e. This gives rise to a tree, and probability measures w on Z\u003csub\u003ep\u003c\/sub\u003e correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L\u003csub\u003e2\u003c\/sub\u003e(Z\u003csub\u003ep\u003c\/sub\u003e,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 L\u003csub\u003e2\u003c\/sub\u003e([-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 GL\u003csub\u003en\u003c\/sub\u003e(q)that interpolates between the p-adic group GL\u003csub\u003en\u003c\/sub\u003e(Z\u003csub\u003ep\u003c\/sub\u003e), and between its real (and complex) analogue -the orthogonal O\u003csub\u003en\u003c\/sub\u003e (and unitary U\u003csub\u003en\u003c\/sub\u003e )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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2008-05-02\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540783787\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-540-78379-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 222\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369715261580,"sku":"9783540783787","price":44.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540783787.jpg?v=1775674132","url":"https:\/\/lateknightbooks.com\/products\/9783540783787","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}