| 期刊全稱(chēng) | Arithmetical Investigations | | 期刊簡(jiǎn)稱(chēng) | Representation Theor | | 影響因子2023 | Shai M. J. Haran | | 視頻video | http://file.papertrans.cn/162/161628/161628.mp4 | | 發(fā)行地址 | Includes supplementary material: | | 學(xué)科分類(lèi) | Lecture Notes in Mathematics | | 圖書(shū)封面 |  | | 影響因子 | .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.p. which are the inverse limit of the finite rings Z/p.n.. This gives rise to a tree, and probability measures w on Z.p. correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L.2.(Z.p.,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.2.([-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.(q)that interpolates between the p-adic group GL.n.(Z.p.), and between its real (and complex) analogue -the orthogonal O.n. (and unitary U.n. )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and be | | Pindex | Book 2008 |
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