# Jack, Hall-Littlewood and Macdonald Polynomials (Contemporary Mathematics)

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### Description

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and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald).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.

### Contents

Part 1. Historic Material: Henry Jack 1917-1978 by B. D. Sleeman Philip Hall by A. O. Morris Dudley Ernest Littlewood by A. O. Morris Ian Macdonald by A. O. Morris The algebra of partitions by I. G. Macdonald On certain symmetric functions by D. E. Littlewood A class of symmetric polynomials with a parameter by H. Jack A class of polynomials in search of a definition, or the symmetric group parametrized by H. Jack Commentary on the previous paper by I. G. Macdonald First letter from Henry Jack to G. de B. Robinson/Second letter reply from G. de B. Robinson to Henry Jack/Third letter from W. N. Everitt to G. de B. Robinson by H. Jack, G. de B. Robinson, and W. N. Everitt Part 2. Research Articles: Well-poised Macdonald functions $W {\lambda}$ and Jackson coefficients $\omega \lambda$ on $BC n$ by H. Coskun and R. A. Gustafson Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry by J. F. van Diejen Quantization, orbifold cohomology, and Cherednik algebras by P. Etingof and A. Oblomkov Triple groups and Cherednik algebras by B. Ion and S. Sahi Coincident root loci and Jack and Macdonald polynomials for special values of the parameters by M. Kasatani, T. Miwa, A. N. Sergeev, and A. P. Veselov Lowering and raising operators for some special orthogonal polynomials by T. H. Koornwinder Factorization of symmetric polynomials by V. B. Kuznetsov and E. K. Sklyanin A method to derive explicit formulas for an elliptic generalization of the Jack polynomials by E. Langmann A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials by M. Lassalle Limits of $BC$-type orthogonal polynomials as the number of variables goes to infinity by A. Okounkov and G. Olshanski A difference-integral representation of Koornwinder polynomials by E. M. Rains Explicit computation of the $q,t$-Littlewood-Richardson coefficients by M. Schlosser A multiparameter summation formula for Riemann theta functions by V. P. Spiridonov Part 3. Vadim Borisovich Kuznetsov 1963-2005: Vadim Borisovich Kuznetsov 1963-2005 by B. D. Sleeman and E. K. Sklyanin.

### Product Details

• ISBN13: 9780821836835
• Format: Paperback
• ID: 9780821836835
• ISBN10: 0821836838

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