LEADER 05981nam 22015375 450 001 9910154750803321 005 20190708092533.0 010 $a1-4008-8249-4 024 7 $a10.1515/9781400882496 035 $a(CKB)3710000000622804 035 $a(MiAaPQ)EBC4738792 035 $a(DE-B1597)467956 035 $a(OCoLC)979836554 035 $a(DE-B1597)9781400882496 035 $a(EXLCZ)993710000000622804 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aThe Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 /$fC. Bushnell, P. C. Kutzko 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1993 215 $a1 online resource (327 pages) $cillustrations 225 0 $aAnnals of Mathematics Studies ;$v311 311 $a0-691-02114-7 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tComments for the reader -- $t1. Exactness and intertwining -- $t2. The structure of simple strata -- $t3. The simple characters of a simple stratum -- $t4. Interlude with Hecke algebra -- $t5. Simple types -- $t6. Maximal types -- $t7. Typical representations -- $t8. Atypical representations -- $tReferences -- $tIndex of notation and terminology 330 $aThis work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here. 410 0$aAnnals of mathematics studies ;$vno. 129. 606 $aRepresentations of groups 606 $aNonstandard mathematical analysis 610 $aAbelian group. 610 $aAbuse of notation. 610 $aAdditive group. 610 $aAffine Hecke algebra. 610 $aAlgebra homomorphism. 610 $aApproximation. 610 $aAutomorphism. 610 $aBijection. 610 $aBlock matrix. 610 $aCalculation. 610 $aCardinality. 610 $aClassical group. 610 $aComputation. 610 $aConjecture. 610 $aConjugacy class. 610 $aContradiction. 610 $aCorollary. 610 $aCoset. 610 $aCritical exponent. 610 $aDiagonal matrix. 610 $aDimension (vector space). 610 $aDimension. 610 $aDiscrete series representation. 610 $aDiscrete valuation ring. 610 $aDivisor. 610 $aEigenvalues and eigenvectors. 610 $aEquivalence class. 610 $aExact sequence. 610 $aExactness. 610 $aExistential quantification. 610 $aExplicit formula. 610 $aExplicit formulae (L-function). 610 $aField extension. 610 $aFinite group. 610 $aFunctor. 610 $aGauss sum. 610 $aGeneral linear group. 610 $aGroup theory. 610 $aHaar measure. 610 $aHarmonic analysis. 610 $aHecke algebra. 610 $aHomomorphism. 610 $aIdentity matrix. 610 $aInduced representation. 610 $aInteger. 610 $aIrreducible representation. 610 $aIsomorphism class. 610 $aIwahori subgroup. 610 $aJordan normal form. 610 $aLevi decomposition. 610 $aLocal Langlands conjectures. 610 $aLocal field. 610 $aLocally compact group. 610 $aMathematics. 610 $aMatrix coefficient. 610 $aMaximal compact subgroup. 610 $aMaximal ideal. 610 $aMultiset. 610 $aNormal subgroup. 610 $aP-adic number. 610 $aPermutation matrix. 610 $aPolynomial. 610 $aProfinite group. 610 $aQuantity. 610 $aRational number. 610 $aReductive group. 610 $aRepresentation theory. 610 $aRequirement. 610 $aResidue field. 610 $aRing (mathematics). 610 $aScientific notation. 610 $aSimple module. 610 $aSpecial case. 610 $aSub"ient. 610 $aSubgroup. 610 $aSubset. 610 $aSupport (mathematics). 610 $aSymmetric group. 610 $aTensor product. 610 $aTerminology. 610 $aTheorem. 610 $aTopological group. 610 $aTopology. 610 $aVector space. 610 $aWeil group. 610 $aWeyl group. 615 0$aRepresentations of groups. 615 0$aNonstandard mathematical analysis. 676 $a512/.2 686 $aSK 340$2rvk 700 $aBushnell$b C., $01126189 702 $aKutzko$b P. C., 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154750803321 996 $aThe Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129$92657528 997 $aUNINA LEADER 06769nam 22006613u 450 001 996464552103316 005 20230221132630.0 010 $a981-16-4095-5 035 $a(CKB)5340000000068377 035 $aEBL6787726 035 $a(OCoLC)1313880904 035 $a(AU-PeEL)EBL6787726 035 $a(MiAaPQ)EBC6787726 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/72797 035 $a(PPN)258302194 035 $a(EXLCZ)995340000000068377 100 $a20220617d2021|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSublinear Computation Paradigm$b[electronic resource] $eAlgorithmic Revolution in the Big Data Era 210 $aSingapore $cSpringer Singapore Pte. Limited$d2021 215 $a1 online resource (403 p.) 300 $aDescription based upon print version of record. 311 $a981-16-4094-7 327 $aIntro -- Preface -- Contents -- Part I Introduction -- 1 What Is the Sublinear Computation Paradigm? -- 1.1 We Are in the Era of Big Data -- 1.2 Theory of Computational Complexity and Polynomial-Time Algorithms -- 1.3 Polynomial-Time Algorithms and Sublinear-Time Algorithms -- 1.3.1 A Brief History of Polynomial-Time Algorithms -- 1.3.2 Emergence of Sublinear-Time Algorithms -- 1.3.3 Property Testing and Parameter Testing -- 1.4 Ways to Decrease Computational Resources -- 1.4.1 Streaming Algorithms -- 1.4.2 Compression -- 1.4.3 Succinct Data Structures 327 $a1.5 Need for the Sublinear Computation Paradigm -- 1.5.1 Sublinear and Polynomial Computation Are Both Important -- 1.5.2 Research Project ABD -- 1.5.3 The Organization of This Book -- References -- Part II Sublinear Algorithms -- 2 Property Testing on Graphs and Games -- 2.1 Introduction -- 2.2 Basic Terms and Definitions for Property Testing -- 2.2.1 Graphs and the Three Models for Property Testing -- 2.2.2 Properties, Distances, and Testers -- 2.3 Important Known Results in Property Testing on Graphs -- 2.3.1 Results for the Dense-Graph Model -- 2.3.2 Results for the Bounded-Degree Model 327 $a2.3.3 Results for the General-Graph Model -- 2.4 Characterization of Testability on Bounded-Degree Digraphs -- 2.4.1 Bounded-Degree Model of Digraphs -- 2.4.2 Monotone Properties and Hereditary Properties -- 2.4.3 Characterizations -- 2.4.4 An Idea to Extend the Characterizations Beyond Monotone and Hereditary -- 2.5 Testable EXPTIME-Complete Games -- 2.5.1 Definitions -- 2.5.2 Testers for Generalized Chess, Shogi, and Xiangqi -- 2.6 Summary -- References -- 3 Constant-Time Algorithms for Continuous Optimization Problems -- 3.1 Introduction -- 3.2 Graph Limit Theory 327 $a3.3 Quadratic Function Minimization -- 3.3.1 Proof of Theorem 3.1 -- 3.4 Tensor Decomposition -- 3.4.1 Preliminaries -- 3.4.2 Proof of Theorem 3.2 -- 3.4.3 Proof of Lemma 3.4 -- 3.4.4 Proof of Lemma 3.5 -- References -- 4 Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programs -- 4.1 Packing and Covering Semidefinite Programs -- 4.2 Applications -- 4.2.1 SDP relaxation for Robust MaxCut -- 4.2.2 Mahalanobis Distance Learning -- 4.2.3 Related Work -- 4.3 General Framework for Packing-Covering SDPs -- 4.4 Scalar Algorithms 327 $a4.4.1 Scalar MWU Algorithm for (Packing-I)-(Covering-I) -- 4.4.2 Scalar Logarithmic Potential Algorithm For (Packing-I)-(Covering-I) -- 4.5 Matrix Algorithms -- 4.5.1 Matrix MWU Algorithm For (Covering-II)-(Packing-II) -- 4.5.2 Matrix Logarithmic Potential Algorithm For (Packing-I)-(Covering-I) -- 4.5.3 Matrix Logarithmic Potential Algorithm For (Packing-II)-(Covering-II) -- References -- 5 Almost Linear Time Algorithms for Some Problems on Dynamic Flow Networks -- 5.1 Introduction -- 5.2 Preliminaries -- 5.3 Objective Functions -- 5.3.1 Objective Functions for the 1-Sink Problem 327 $a5.3.2 Objective Functions for k-Sink 330 $aThis open access book gives an overview of cutting-edge work on a new paradigm called the ?sublinear computation paradigm,? which was proposed in the large multiyear academic research project ?Foundations of Innovative Algorithms for Big Data.? That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as ?fast,? but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms. 606 $aAlgorithms & data structures$2bicssc 606 $aNumerical analysis$2bicssc 610 $aSublinear Algorithms 610 $apolynomial time algorithms 610 $aConstant-Time Algorithms 610 $aSublinear Computation Paradigm 610 $aopen access 615 7$aAlgorithms & data structures 615 7$aNumerical analysis 700 $aKatoh$b Naoki$01238685 701 $aHigashikawa$b Yuya$01238686 701 $aIto$b Hiro$01238687 701 $aNagao$b Atsuki$01238688 701 $aShibuya$b Tetsuo$01238689 701 $aSljoka$b Adnan$01238690 701 $aTanaka$b Kazuyuki$01238691 701 $aUno$b Yushi$01073569 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a996464552103316 996 $aSublinear Computation Paradigm$92874616 997 $aUNISA