Algebraic Methods And Q Special Functions

Author : Jan Felipe Van Diejen
Publisher : American Mathematical Soc.
ISBN 13 : 0821820265
Total Pages : 290 pages
Book Rating : 4.61/5 ( download)

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Download or read book Algebraic Methods and $q$-Special Functions written by Jan Felipe Van Diejen and published by American Mathematical Soc.. This book was released on 1999 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Author : Jan Felipe Van Diejen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873298
Total Pages : 302 pages
Book Rating : 4.96/5 ( download)

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Download or read book Algebraic Methods and Q-special Functions written by Jan Felipe Van Diejen and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Author : Mourad Ismail
Publisher : American Mathematical Soc.
ISBN 13 : 082180524X
Total Pages : 289 pages
Book Rating : 4.44/5 ( download)

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Download or read book Special Functions, $q$-Series and Related Topics written by Mourad Ismail and published by American Mathematical Soc.. This book was released on 1997 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions from the proceedings at The Fields Institute workshop on Special Functions, q-Series and Related Topics that was held in June 1995. The articles cover areas from quantum groups and their representations, multivariate special functions, q-series, and symbolic algebra techniques as well as the traditional areas of single-variable special functions. The book contains both pure and applied topics and reflects recent trends of research in the various areas of special functions.

Author : Joaquin Bustoz
Publisher : Springer Science & Business Media
ISBN 13 : 9401008183
Total Pages : 521 pages
Book Rating : 4.81/5 ( download)

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Download or read book Special Functions 2000: Current Perspective and Future Directions written by Joaquin Bustoz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.

Author : George E. Andrews
Publisher : Cambridge University Press
ISBN 13 : 9780521789882
Total Pages : 684 pages
Book Rating : 4.85/5 ( download)

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Download or read book Special Functions written by George E. Andrews and published by Cambridge University Press. This book was released on 1999 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Author : H. Crapo
Publisher : Springer Science & Business Media
ISBN 13 : 9788847000780
Total Pages : 564 pages
Book Rating : 4.85/5 ( download)

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Download or read book Algebraic Combinatorics and Computer Science written by H. Crapo and published by Springer Science & Business Media. This book was released on 2001-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Author : Jiri Patera
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951256
Total Pages : 284 pages
Book Rating : 4.53/5 ( download)

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Download or read book Algebraic Methods in Physics written by Jiri Patera and published by Springer Science & Business Media. This book was released on 2001 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-Similarities and Invariant Densities for Model Sets.- Model Sets and Self-Similarities.- Averaging Operators and Invariant Densities.- Further Remarks.- Outlook.- References.- Symmetry Operations in the Brain: Music and Reasoning.- Trion Model.- Music Enhances Spatial-Temporal Reasoning.- References.- Lie Modules of Bounded Multiplicities.- Simple L Modules with Finite-Dimensional Weight Spaces.- Completely Pointed Modules.- Completely Pointed Modules Tensored with Finite-Dimensional Modules.- References.- Moving Frames and Coframes.- References.- The Fibonacci-Deformed Harmonic Oscillator.- About Strictly Increasing Sequences of Positive Numbers.- Quantum Algebra Associated with the Spectrum ? = xn.- The ?-Natural Spectrum.- The Fibonacci Deformation of Weyl Algebra.- Coherent States and Some Special Functions.- References.- Continuous and Discrete Linearizable Systems: The Riccati Saga.- Brief Review of the Continuous Gambier Equation.- Discrete Analog of the Gambier Equation, Revisited.- Discrete Projective and Matrix Riccati Equations.- Discrete Conformai Riccati Equations.- Conclusions and Outlook.- References.- Superintegrability on Two-Dimensional Complex Euclidean Space.- Potential V5.- Potential V6.- Potential V7.- References.- Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds.- Hydrodynamic Systems Rich in Conservation Laws.- Applications of the Higher-Dimensional Laplace Transformation to Hydrodynamic Systems that are Rich in Conservation Laws.- References.- Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras.- Simple and Affine Lie Algebras.- Branching Rules for Simple Lie Algebras.- Young Diagrams and Branching Rules.- Weight Multiplicities of Simple Lie Algebras.- Young Tableaux and Weight Multiplicities.- Branching Rule Multiplicities for the Restriction from Affine to Simple Lie Algebras.- Branching Rules Derived from Characters.- Weight Multiplicities of Affine Lie Algebras.- References.- Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice.- Construction of the Classifying Conditions.- The Toda Lattice Class.- References.- Complete Description of the Voronoï Cell of the Lie Algebra An Weight Lattice. On the Bounds for the Number of d-Faces of the n-Dimensional Voronoï Cells.- The Expression of the Bounds Nd(n) Obtained by Voronoï.- Detailed Description of the Voronoï Cells of the A(TM) Lattices.- The New Explicit Expression of Bounds Nd(n).- Expression of Nd(n) as Multiple of a Stirling Number of Second Kind.- Final Remarks.- References.- The Relativistic Oscillator and the Mass Spectra of Baryons.- The System of Three Relativistic Scalar Particles with Oscillator Interactions.- An Approach to the Spinorial Relativistic Three-Body System.- References.- Seiberg-Witten Theory Without Tears.- N = 2 Supersymmetry.- N = 2 Superaction.- Textbook Properties.- Spontaneous Symmetry-Breaking.- Holomorphy and Duality.- Perturbative and Nonperturbative F (A).- Preliminaries.- Fuchsian Maps.- The Schwarzian Derivatives.- SW Choice.- Correctness.- Uniqueness.- References.- Bargmann Representation for Some Deformed Harmonic Oscillators with Non-Fock Representation.- Representations.- Toward a Bargmann Representation.- The "q-Oscillator".- Generalization of the Previous Example.- Deformed Algebra Associated to a Given Weight function.- Bargmann Representations Corresponding to Different ?.- The Case of an Annulus.- Conclusion.- References.- The Vector-Coherent-State Inducing Construction for Clebsch-Gordan Coefficients.- Induced Representations of su(4).- SU(4) Clebsch-Gordan Coefficients.- Summary.- References.- Highest-Weight Representations of Borcherds Algebras.- Borcherds Algebras.- Cartan Subalgebra of an Affine Kac-Moody Algebra.- Adding Energy and Number Operators to the Cartan Subalgebra.- Conclusions.- References.- Graded Contractions of Lie Algebras of Physical Interest.- Notion of Graded

Author : Erik Koelink
Publisher : Springer
ISBN 13 : 3540449450
Total Pages : 259 pages
Book Rating : 4.54/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by Erik Koelink and published by Springer. This book was released on 2003-07-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.

Author : Thomas Lam
Publisher : Springer
ISBN 13 : 1493906828
Total Pages : 226 pages
Book Rating : 4.26/5 ( download)

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Download or read book k-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by Springer. This book was released on 2014-06-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.

Author : B. Brent Gordon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870204
Total Pages : 468 pages
Book Rating : 4.03/5 ( download)

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Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.