对称函数和正交多项式（影印版）
作者： I.G.Macdonald
出版时间：2020-04
出版社：高等教育出版社
- 高等教育出版社
- 9787040535938
- 1版
- 296653
- 46254131-9
- 精装
- 16开
- 2020-04
- 120
- 76
- 理学
- 数学
- 数学类
- 研究生及以上
前辅文
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 Px(q，t)
12.Further properties of the Px(q，t)
Chapter 2.Orthogonal Polynomials
1.Introduction
2.Root systems
3.Orbit sums and Weyl characters
4.Scalar product
5.The polynomials Px
6.Proof of the existence theorem
7.Proof of the existence theorem，concluded
8.Some properties of the Px
9.The general case
Chapter 3.Postscript
1.The a fine root system and the extended a fine Weyl group
2.The braid group
3.The a fine Hecke algebra
4.Cherednik's scalar product
5.Another proof of the existence theorem
6.The nonsymmetric polynomials Ex
7.Calculation of(Px，Px)
8.The double affine Hecke algebra and duality
9.The Fourier transform
10.The general case
References
