**University Lecture Series**

Volume: 12;
1998;
53 pp;
Softcover

MSC: Primary 05; 22; 33;

Print ISBN: 978-0-8218-0770-5

Product Code: ULECT/12

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

**Electronic ISBN: 978-1-4704-2161-8
Product Code: ULECT/12.E**

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

# Symmetric Functions and Orthogonal Polynomials

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*I. G. Macdonald*

One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

#### Readership

Graduate students and research mathematicians interested in combinatorics.

#### Reviews & Endorsements

Can serve as a self-contained introduction for anyone with some background in symmetric functions and root systems.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Symmetric Functions and Orthogonal Polynomials

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface ix10 free
- Introduction xi12 free
- Chapter 1. Symmetric Functions 118 free
- 1. The ring of symmetric functions 118
- 2. Monomial symmetric functions 219
- 3. Elementary symmetric functions 320
- 4. Complete symmetric functions 320
- 5. Power sums 421
- 6. Scalar product 522
- 7. Schur functions 724
- 8. Zonal polynomials 1027
- 9. Jack's symmetric functions 1128
- 10. Hall-Littlewood symmetric functions 1128
- 11. The symmetric functions Pλ (q,t) 1229
- 12. Further properties of the Pλ (q,t) 1835

- Chapter 2. Orthogonal Polynomials 2340
- Chapter 3. Postscript 3956
- 1. The affine root system and the extended affine Weyl group 3956
- 2. The braid group 4057
- 3. The affine Hecke algebra 4158
- 4. Cherednik's scalar product 4360
- 5. Another proof of the existence theorem 4461
- 6. The nonsymmetric polynomials Eλ 4663
- 7. Calculation of (P[sub(λ)], P[sub(λ)]) 4764
- 8. The double affine Hecke algebra and duality 4865
- 9. The Fourier transform 5067
- 10. The general case 5269

- References 5370
- Back Cover Back Cover171