{"product_id":"arithmetical-investigations-representation-theory-orthogonal-polynomials-and-quantum-interpolations-von-shai-m-j-haran","title":"Arithmetical Investigations","description":"\n                                \n                \u003cp\u003e\n                                        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 Z\n                    \n                    \u003csub\u003ep\u003c\/sub\u003e\n                                         which are the inverse limit of the finite rings Z\/p\n                    \n                    \u003csup\u003en\u003c\/sup\u003e\n                                        . This gives rise to a tree, and probability measures w on Z\n                    \n                    \u003csub\u003ep\u003c\/sub\u003e\n                                         correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L\n                    \n                    \u003csub\u003e2\u003c\/sub\u003e\n                                        (Z\n                    \n                    \u003csub\u003ep\u003c\/sub\u003e\n                                        ,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\n                    \n                    \u003csub\u003e2\u003c\/sub\u003e\n                                        ([-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\n                    \n                    \u003csub\u003en\u003c\/sub\u003e\n                                        (q)that interpolates between the p-adic group GL\n                    \n                    \u003csub\u003en\u003c\/sub\u003e\n                                        (Z\n                    \n                    \u003csub\u003ep\u003c\/sub\u003e\n                                        ), and between its real (and complex) analogue -the orthogonal O\n                    \n                    \u003csub\u003en\u003c\/sub\u003e\n                                         (and unitary U\n                    \n                    \u003csub\u003en\u003c\/sub\u003e\n                                         )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.\n                \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540783787\"\u003e\u003ch3\u003eRepresentation Theory, Orthogonal Polynomials, and Quantum Interpolations\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783540783787","offer_id":39436946440285,"sku":"9783540783787","price":37.4,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/b2f25777-13ac-428e-859b-ee23cb3841db.jpg?v=1772085310","url":"https:\/\/shop.autorenwelt.de\/en\/products\/arithmetical-investigations-representation-theory-orthogonal-polynomials-and-quantum-interpolations-von-shai-m-j-haran","provider":"Autorenwelt Shop","version":"1.0","type":"link"}