LEADER 03420nam 22005175 450 001 996466535803316 005 20200706192224.0 010 $a3-540-78379-2 024 7 $a10.1007/978-3-540-78379-4 035 $a(CKB)1000000000437232 035 $a(SSID)ssj0000316330 035 $a(PQKBManifestationID)11225812 035 $a(PQKBTitleCode)TC0000316330 035 $a(PQKBWorkID)10263930 035 $a(PQKB)11498750 035 $a(DE-He213)978-3-540-78379-4 035 $a(MiAaPQ)EBC3068723 035 $a(PPN)125218338 035 $a(EXLCZ)991000000000437232 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aArithmetical Investigations$b[electronic resource] $eRepresentation Theory, Orthogonal Polynomials, and Quantum Interpolations /$fby Shai M. J. Haran 205 $a1st ed. 2008. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2008. 215 $axii, 217 p. $cill 225 1 $aLecture Notes in Mathematics,$x0075-8434 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-78378-4 320 $aIncludes bibliographical references (p. [209]-213) and index. 327 $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. 330 $aIn this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums. 410 0$aLecture Notes in Mathematics,$x0075-8434 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a511.42 700 $aHaran$b Shai M. J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0724875 906 $aBOOK 912 $a996466535803316 996 $aArithmetical investigations$91416595 997 $aUNISA