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001			978-3-540-78379-4
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020			_a9783540783794 _9978-3-540-78379-4
024	7		_a10.1007/978-3-540-78379-4 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
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.
260		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v1941
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	_aMathematics.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
700	1		_aHaran, Shai M. J. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540783787
786			_dSpringer
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v1941
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-78379-4
942			_2EBK1893 _cEBK
999			_c31187 _d31187