000 | 03273nam a22004455i 4500 | ||
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001 | 978-3-540-78379-4 | ||
003 | DE-He213 | ||
005 | 20190213151259.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2008 gw | s |||| 0|eng d | ||
020 |
_a9783540783794 _9978-3-540-78379-4 |
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024 | 7 |
_a10.1007/978-3-540-78379-4 _2doi |
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050 | 4 | _aQA241-247.5 | |
072 | 7 |
_aPBH _2bicssc |
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_aMAT022000 _2bisacsh |
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_aPBH _2thema |
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082 | 0 | 4 |
_a512.7 _223 |
245 | 1 | 0 |
_aArithmetical Investigations _h[electronic resource] : _bRepresentation Theory, Orthogonal Polynomials, and Quantum Interpolations / _cedited by Shai M. J. Haran. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008. |
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300 |
_aXII, 222 p. 23 illus. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 |
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505 | 0 | _aIntroduction: 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. | |
520 | _aIn 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. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )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. | ||
650 | 0 | _aNumber theory. | |
650 | 1 | 4 |
_aNumber Theory. _0http://scigraph.springernature.com/things/product-market-codes/M25001 |
700 | 1 |
_aHaran, Shai M. J. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540849216 |
776 | 0 | 8 |
_iPrinted edition: _z9783540783787 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-540-78379-4 |
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912 | _aZDB-2-LNM | ||
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