Electronic ISBN:  9780821880968 
Product Code:  CONM/417.E 
List Price:  $105.00 
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AMS Member Price:  $84.00 

Book DetailsContemporary MathematicsVolume: 417; 2006; 360 ppMSC: Primary 33;
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, farreaching 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, HallLittlewood 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and Macdonald; the original papers of Littlewood and Jack; notes on Hall's work by Macdonald; and a recently discovered unpublished manuscript by Jack (annotated by Macdonald).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.ReadershipResearch mathematicians interested in algebraic combinatorics.

Table of Contents

Part 1. Historical Material [ MR 2284114 ]

B. D. Sleeman  Henry Jack 1917–1978 [ MR 2283247 ]

Alun O. Morris  Philip Hall [ MR 2284116 ]

Alun O. Morris  Dudley Ernest Littlewood [ MR 2284117 ]

Alun O. Morris  Ian Macdonald [ MR 2284118 ]

Edited by Vadim B. Kuznetsov and Siddhartha Sahi  I. G. Macdonald – The algebra of partitions (This article is not available individually due to permission restrictions; to view, see the <a href = "conm417.pdf">full volume PDF</a>.) [ MR 2284114 ]

D. E. Littlewood  On certain symmetric functions [ MR 2284120 ]

Henry Jack  A class of symmetric polynomials with a parameter [ MR 2284121 ]

Henry Jack  A class of polynomials in search of a definition, or the symmetric group parametrized [ MR 2284122 ]

I. G. Macdonald  Commentary on the previous paper: “A class of polynomials in search of a definition, or the symmetric group parametrized” [in Jack, HallLittlewood and Macdonald polynomials, 75–106, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006; MR2284122] by H. Jack [ MR 2284123 ]

Henry Jack  First letter from Henry Jack to G. de B. Robinson [ MR 2284124 ]

Part 2. Research Articles [ MR 2284114 ]

Hasan Coskun and Robert A. Gustafson  Wellpoised Macdonald functions $W_\lambda $ and Jackson coefficients $\omega _\lambda $ on $BC_n$ [ MR 2284125 ]

J. F. van Diejen  Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry [ MR 2284126 ]

Pavel Etingof and Alexei Oblomkov  Quantization, orbifold cohomology, and Cherednik algebras [ MR 2284127 ]

Bogdan Ion and Siddhartha Sahi  Triple groups and Cherednik algebras [ MR 2284128 ]

M. Kasatani, T. Miwa, A. N. Sergeev and A. P. Veselov  Coincident root loci and Jack and Macdonald polynomials for special values of the parameters [ MR 2284129 ]

Tom H. Koornwinder  Lowering and raising operators for some special orthogonal polynomials [ MR 2284130 ]

Vadim B. Kuznetsov and Evgeny K. Sklyanin  Factorization of symmetric polynomials [ MR 2284131 ]

Edwin Langmann  A method to derive explicit formulas for an elliptic generalization of the Jack polynomials [ MR 2284132 ]

Michel Lassalle  A short proof of generalized JacobiTrudi expansions for Macdonald polynomials [ MR 2284133 ]

Andrei Okounkov and Grigori Olshanski  Limits of $BC$type orthogonal polynomials as the number of variables goes to infinity [ MR 2284134 ]

Eric M. Rains  A differenceintegral representation of Koornwinder polynomials [ MR 2284135 ]

Michael Schlosser  Explicit computation of the $q,t$LittlewoodRichardson coefficients [ MR 2284136 ]

Vyacheslav P. Spiridonov  A multiparameter summation formula for Riemann theta functions [ MR 2284137 ]

Part 3. Vadim Kuznetsov 1963–2005 [ MR 2284114 ]

Evgeny Sklyanin and Brian D. Sleeman  Vadim Borisovich Kuznetsov 1963–2005 [ MR 2284138 ]


Additional Material

Reviews

The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.
Zentralblatt MATH


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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, farreaching 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, HallLittlewood 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.
Research mathematicians interested in algebraic combinatorics.

Part 1. Historical Material [ MR 2284114 ]

B. D. Sleeman  Henry Jack 1917–1978 [ MR 2283247 ]

Alun O. Morris  Philip Hall [ MR 2284116 ]

Alun O. Morris  Dudley Ernest Littlewood [ MR 2284117 ]

Alun O. Morris  Ian Macdonald [ MR 2284118 ]

Edited by Vadim B. Kuznetsov and Siddhartha Sahi  I. G. Macdonald – The algebra of partitions (This article is not available individually due to permission restrictions; to view, see the <a href = "conm417.pdf">full volume PDF</a>.) [ MR 2284114 ]

D. E. Littlewood  On certain symmetric functions [ MR 2284120 ]

Henry Jack  A class of symmetric polynomials with a parameter [ MR 2284121 ]

Henry Jack  A class of polynomials in search of a definition, or the symmetric group parametrized [ MR 2284122 ]

I. G. Macdonald  Commentary on the previous paper: “A class of polynomials in search of a definition, or the symmetric group parametrized” [in Jack, HallLittlewood and Macdonald polynomials, 75–106, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006; MR2284122] by H. Jack [ MR 2284123 ]

Henry Jack  First letter from Henry Jack to G. de B. Robinson [ MR 2284124 ]

Part 2. Research Articles [ MR 2284114 ]

Hasan Coskun and Robert A. Gustafson  Wellpoised Macdonald functions $W_\lambda $ and Jackson coefficients $\omega _\lambda $ on $BC_n$ [ MR 2284125 ]

J. F. van Diejen  Asymptotics of multivariate orthogonal polynomials with hyperoctahedral symmetry [ MR 2284126 ]

Pavel Etingof and Alexei Oblomkov  Quantization, orbifold cohomology, and Cherednik algebras [ MR 2284127 ]

Bogdan Ion and Siddhartha Sahi  Triple groups and Cherednik algebras [ MR 2284128 ]

M. Kasatani, T. Miwa, A. N. Sergeev and A. P. Veselov  Coincident root loci and Jack and Macdonald polynomials for special values of the parameters [ MR 2284129 ]

Tom H. Koornwinder  Lowering and raising operators for some special orthogonal polynomials [ MR 2284130 ]

Vadim B. Kuznetsov and Evgeny K. Sklyanin  Factorization of symmetric polynomials [ MR 2284131 ]

Edwin Langmann  A method to derive explicit formulas for an elliptic generalization of the Jack polynomials [ MR 2284132 ]

Michel Lassalle  A short proof of generalized JacobiTrudi expansions for Macdonald polynomials [ MR 2284133 ]

Andrei Okounkov and Grigori Olshanski  Limits of $BC$type orthogonal polynomials as the number of variables goes to infinity [ MR 2284134 ]

Eric M. Rains  A differenceintegral representation of Koornwinder polynomials [ MR 2284135 ]

Michael Schlosser  Explicit computation of the $q,t$LittlewoodRichardson coefficients [ MR 2284136 ]

Vyacheslav P. Spiridonov  A multiparameter summation formula for Riemann theta functions [ MR 2284137 ]

Part 3. Vadim Kuznetsov 1963–2005 [ MR 2284114 ]

Evgeny Sklyanin and Brian D. Sleeman  Vadim Borisovich Kuznetsov 1963–2005 [ MR 2284138 ]

The book will be invaluable to students and researchers who wish to learn about this beautiful and exciting subject.
Zentralblatt MATH