LEADER 01292nam--2200397---450- 001 990002077940203316 005 20091106101707.0 010 $a978-88-370-6900-1 035 $a000207794 035 $aUSA01000207794 035 $a(ALEPH)000207794USA01 035 $a000207794 100 $a20041013d2009----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $aa|||||||001yy 200 1 $aGranet$eRoma e Parigi, la natura romantica$fa cura di Anna Ottani Cavina$gcon la collaborazione di Marc Bayard e Bernard Terlay 210 $aRoma$cAcadémie de France à Rome$aMilano$cElecta$d2009 215 $a127 p.$cill.$d26 cm 300 $aCatalogo della mostra tenuta a Roma nel 2009 600 1$aGranet,$bFrançois Marius$xCataloghi di esposizioni$2BNCF 676 $a759.4 702 1$aOTTANI CAVINA,$bAnna 702 1$aBAYARD,$bMarc 702 1$aTERLAY,$bBernard 702 1$aGRANET,$bFrançois Marius 801 0$aIT$bsalbc$gISBD 912 $a990002077940203316 951 $aXII.2.C. 1832$b2183 L.G.$cXII.2.C.$d00260320 959 $aBK 969 $aUMA 979 $aACQUISTI$b10$c20041013$lUSA01$h1450 979 $aANNAMARIA$b90$c20091106$lUSA01$h0844 979 $aANNAMARIA$b90$c20091106$lUSA01$h1017 996 $aGranet$9148837 997 $aUNISA LEADER 05230nam 2200637 a 450 001 9910789068503321 005 20230725052611.0 010 $a1-283-43383-4 010 $a9786613433831 010 $a981-4350-72-9 035 $a(CKB)3400000000016747 035 $a(EBL)840615 035 $a(OCoLC)858228500 035 $a(SSID)ssj0000644804 035 $a(PQKBManifestationID)12255385 035 $a(PQKBTitleCode)TC0000644804 035 $a(PQKBWorkID)10680253 035 $a(PQKB)11718938 035 $a(MiAaPQ)EBC840615 035 $a(WSP)00008161 035 $a(Au-PeEL)EBL840615 035 $a(CaPaEBR)ebr10524594 035 $a(CaONFJC)MIL343383 035 $a(EXLCZ)993400000000016747 100 $a20110823d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplications of unitary symmetry and combinatorics$b[electronic resource] /$fJames D. Louck 210 $aHackensack, N.J. $cWorld Scientific$dc2011 215 $a1 online resource (381 p.) 300 $aDescription based upon print version of record. 311 $a981-4350-71-0 320 $aIncludes bibliographical references and index. 327 $aPreface and Prelude; OVERVIEW AND SYNTHESIS OF BINARY COUPLING THEORY; TOPICAL CONTENTS; MATTERS OF STYLE, READERSHIP, AND RECOGNITION; Contents; Notation; 1 Composite Quantum Systems; 1.1 Introduction; 1.2 Angular Momentum State Vectors of a Composite System; 1.2.1 Group Actions in a Composite System; 1.3 Standard Form of the Kronecker Direct Sum; 1.3.1 Reduction of Kronecker Products; 1.4 Recoupling Matrices; 1.5 Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices; 1.6 Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory 327 $a2 Algebra of Permutation Matrices2.1 Introduction; 2.2 Basis Sets of Permutation Matrices; 2.2.1 Summary; 3 Coordinates of A in Basis P n(e,p); 3.1 Notations; 3.2 The A-Expansion Rule in the Basis P n(e,p); 3.3 Dual Matrices in the Basis Set ?n(e, p); 3.3.1 Dual Matrices for ?3(e, p); 3.3.2 Dual Matrices for ?4(e, p); 3.4 The General Dual Matrices in the Basis ?n(e, p); 3.4.1 Relation between the A-Expansion and Dual Matrices; 4 Further Applications of Permutation Matrices; 4.1 Introduction; 4.2 An Algebra of Young Operators; 4.3 Matrix Schur Functions 327 $a4.4 Real Orthogonal Irreducible Representations of Sn4.4.1 Matrix Schur Function Real Orthogonal Irreducible Representations; 4.4.2 Jucys-Murphy Real Orthogonal Representations; 4.5 Left and Right Regular Representations of Finite Groups; 5 Doubly Stochastic Matrices in Angular Momentum Theory; 5.1 Introduction; 5.2 Abstractions and Interpretations; 5.3 Permutation Matrices as Doubly Stochastic; 5.4 The Doubly Stochastic Matrix for a Single System with Angular Momentum J; 5.4.1 Spin-1/2 System; 5.4.2 Angular Momentum-j System 327 $a5.5 Doubly Stochastic Matrices for Composite Angular Momentum Systems5.5.1 Pair of Spin-1/2 Systems; 5.5.2 Pair of Spin-1/2 Systems as a Composite System; 5.6 Binary Coupling of Angular Momenta; 5.6.1 Complete Sets of Commuting Hermitian Observables; 5.6.2 Domain of Definition RT (j); 5.6.3 Binary Bracketings, Shapes, and Binary Trees; 5.7 State Vectors: Uncoupled and Coupled; 5.8 General Binary Tree Couplings and Doubly Stochastic Matrices; 5.8.1 Overview; 5.8.2 Uncoupled States; 5.8.3 Generalized WCG Coefficients; 5.8.4 Binary Tree Coupled State Vectors 327 $a5.8.5 Racah Sum-Rule and Biedenharn-Elliott Identity as Transition Probability Amplitude Relations5.8.6 Symmetries of the 6 - j and 9 - j Coefficients; 5.8.7 General Binary Tree Shape Transformations; 5.8.8 Summary; 5.8.9 Expansion of Doubly Stochastic Matrices into Permutation Matrices; 6 Magic Squares; 6.1 Review; 6.2 Magic Squares and Addition of Angular Momenta; 6.3 Rational Generating Function of Hn(r); 7 Alternating Sign Matrices; 7.1 Introduction; 7.2 Standard Gelfand-Tsetlin Patterns; 7.2.1 A-Matrix Arrays; 7.2.2 Strict Gelfand-Tsetlin Patterns 327 $a7.3 Strict Gelfand-Tsetlin Patterns for ? = (n n . 1 · · · 2 1) 330 $aThis monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrice 606 $aSymmetry (Physics) 606 $aCombinatorial analysis 615 0$aSymmetry (Physics) 615 0$aCombinatorial analysis. 676 $a511.6 700 $aLouck$b James D$044887 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789068503321 996 $aApplications of unitary symmetry and combinatorics$93822321 997 $aUNINA