Jack, Hall-Littlewood and Macdonald Polynomials.

Intro -- Contents -- Preface -- Bibliography -- Acknowledgments -- Part 1. Historic Material -- Photo of Henry Jack -- Henry Jack 1917-1978 -- Photo of Philip Hall -- Philip Hall -- Photo of Dudley Ernest Littlewood -- Dudley Ernest Littlewood -- Photo of Ian Macdonald -- Ian Macdonald -- The Algebra of Partitions -- 1. Introduction -- 2. The algebra of symmetric functions -- 3. Hall polynomials and the Hall algebra -- 4. Hall-Littlewood symmetric functions -- 5. GLn over a finite field -- 6. GLn over a local field -- 7. Concluding remarks -- References -- On Certain Symmetric Functions -- A class of symmetric polynomials with a parameter -- A class of polynomials in search of a definition, or the symmetric group parametrized -- Commentary on the previous paper -- First letter from Henry Jack to G. de B. Robinson [16.4.76] -- Part 2. Research articles -- Well-poised Macdonald functions Wλ and Jackson coefficients ωλ on BCn -- Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry -- Quantization, orbifold cohomology, and Cherednik algebras -- Triple groups and Cherednik algebras -- Coincident root loci and Jack and Macdonald polynomials for special values of the parameters -- Lowering and raising operators for some special orthogonal polynomials -- Factorization of symmetric polynomials -- A method to derive explicit formulas for an elliptic generalization of the Jack polynomials -- A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials -- Limits of BC-type orthogonal polynomials as the number of variables goes to infinity -- 1. Introduction -- 1A. BCn orthogonal polynomials -- 1B. Statement of the main result -- 1C. Other results -- 2. Interpolation BCn polynomials and binomial formula -- 2A. Interpolation BCn polynomials -- 2B. Binomial formula.

2C. Asymptotics of denominators in binomial formula -- 3. Sufficient conditions of regularity -- 4. Necessary conditions of regularity -- 5. The convex set γθ -- 6. Spherical functions on infinite-dimensional symmetric spaces -- 7. The BCn polynomials with θ = 1 -- References -- A difference-integral representation of Koornwinder polynomials -- Explicit computation of the q, t-Littlewood-Richardson coefficients -- A multiparameter summation formula for Riemann theta functions -- Part 3. Vadim Kuznetsov 1963-2005 -- Photo of Vadim Kuznetsov -- Vadim Borisovich Kuznetsov 1963-2005.

The subject of symmetric functions began with the work of Jacobi, Schur, Weyl, Young and others on the Schur polynomials. In the 1950's and 60's, far-reaching generalizations of Schur polynomials were obtained by Hall and Littlewood (independently) and, in a different direction, by Jack. In the 1980's, Macdonald unified these developments by introducing a family of polynomials associated with arbitrary root systems.The last twenty years have witnessed considerable progress in this area, revealing new and profound connections with representation theory, algebraic geometry, combinatorics, special functions, classical analysis and mathematical physics. All these fields and more are represented in this volume, which contains the proceedings of a conference on "Jack, Hall-Littlewood and Macdonald polynomials" held at ICMS, Edinburgh, during September 23-26, 2003.In addition to new results by leading researchers, the book contains a wealth of historical material, including brief biographies of Hall, Littlewood, Jack and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald). The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.