作者：IGMacdonald[著]
页数：76
出版社：高等教育出版社
出版日期：2016
ISBN：9787040535938
电子书格式：PDF
PDF下载地址
内容简介
作为代数学的最经典领域之一，对称函数和正交多项式理论与组合学、表示论以及其他数学分支相关联已久为人知，Macdonald或许是该领域的作者，基于其在Rutgers大学的讲义，本书解释了这些关联的一些新近进展。特别地，本书给出了与仿射Hecke代数相伴的正交多项式的第一结果，概述了一些著名的组合猜想的证明。本书适合于对组合学感兴趣的研究生阅读，也可供相关研究人员参考。
目录
Preface
Introduction
Symmetric functions
Schur functions and their generalizations
Jacobi polynomials attached to root systems
Constant term identities
References
Chapter 1.Symmetric Functions
1.The ring of symmetric functions
2.Monomial symmetric functions
3.Elementary symmetric functions
4.Complete symmetric functions
5.Power sums
6.Scalar product
7.Schur functions
8.Zonal polynomials
9.Jack’s symmetric functions
10.Hall-Littlewood symmetric functions
11.The symmetric functions Pλ(q, t)
12.Fhrther properties of the Pλ(q, t)
Chapter 2.Orthogonal Polynomials
1.Introduction
2.Root systems
3.Orbit sums and Weyl characters
4.Scalar product
5.The polynomials Pλ
6.Proof of the existence theorem
7.Proof of the existence theorem, concluded
8.Some properties of the Pλ
9.The general case
Chapter 3.Postscript
1.The affine root system and the extended affine Weyl group
2.The braid group
3.The affine Hecke algebra
4.Cherednik’s scalar product
5.Another proof of the existence theorem
6.The nonsymmetric polynomials Eλ
7.Calculation of (Pλ, Pλ)
8.The double affine Hecke algebra and duality
9.The Fourier transform
10.The general case
References
Introduction
Symmetric functions
Schur functions and their generalizations
Jacobi polynomials attached to root systems
Constant term identities
References
Chapter 1.Symmetric Functions
1.The ring of symmetric functions
2.Monomial symmetric functions
3.Elementary symmetric functions
4.Complete symmetric functions
5.Power sums
6.Scalar product
7.Schur functions
8.Zonal polynomials
9.Jack’s symmetric functions
10.Hall-Littlewood symmetric functions
11.The symmetric functions Pλ(q, t)
12.Fhrther properties of the Pλ(q, t)
Chapter 2.Orthogonal Polynomials
1.Introduction
2.Root systems
3.Orbit sums and Weyl characters
4.Scalar product
5.The polynomials Pλ
6.Proof of the existence theorem
7.Proof of the existence theorem, concluded
8.Some properties of the Pλ
9.The general case
Chapter 3.Postscript
1.The affine root system and the extended affine Weyl group
2.The braid group
3.The affine Hecke algebra
4.Cherednik’s scalar product
5.Another proof of the existence theorem
6.The nonsymmetric polynomials Eλ
7.Calculation of (Pλ, Pλ)
8.The double affine Hecke algebra and duality
9.The Fourier transform
10.The general case
References