新書推薦：
《
时间的朋友
》
售價：NT$
301
《
士变：近代中国的思想转折
》
售價：NT$
449
《
本土在行动：近代中国的疾病、医疗与卫生（1820-1937）（学衡心史文丛）
》
售價：NT$
500
《
生活中的逻辑学
》
售價：NT$
347
《
天下无讼
》
售價：NT$
352
《
春台记事 盛晚风
》
售價：NT$
356
《
科学与现代世界：现代科学的起源 怀特海全集系列
》
售價：NT$
459
《
康有为对“君民共主”宪法概念的建构
》
售價：NT$
449
|
| 內容簡介： |
|
The ring of symmetric functions A， with natural basis given by the Schur functions， arise in many different areas of mathematics. For example， as the cohomology ring of the grassmanian， and as the representation ring of the symmetric group. One may define a coproduct on A by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood-Richardson numbers may be viewed as the structure constants for the co-product in the Schur basis. The first part of this thesis， inspired by the umbral calculus of Gian-Carlo Rota， is a study of the co-algebra maps of A， The Macdonald polynomials are a somewhat mysterious qt-deformation of the Schur functions. The second part of this thesis contains a proof a generating function identity for the Macdonald polynomials which was originally conjectured by Kawanaka.
|
| 目錄：
|
1．Symmetric functions of Littlewood-Richardson type
1．1．Symmetric Functions
1．1．1．Partitions
1．1．2．Monomial syrmnetric functions
1．1．3．Plethystic notation
1．1．4．Schur functions
1．2．The Umbral Calculus
1．2．1．Coalgebras
1．2．2．Sequences of Binomial Type
1．3．The Hall inner-product
1．3．1．Preliminaries
1．3．2．Column operators
1．3．3．Duality
1．4．Littlewood-Richardson Bases
1．4．1．Generalized complete symmetric functions
1．4．2．Umbraloperators
1．4．3．Column operators
1．4．4．Generalized elementary symmetric functions
1．5．Examples
2．A generating function identity for Macdonald polynomials
2．1．Macdonald Polynomials
2．1．1 ．Notation
2．1．2．Operator definition
2．1．3．Characterization using the inner product
2．1．4．Arms and legs
2．1．5．Duality
2．1．6．Kawanaka conjecture
2．2．Resultants
2．2．1．Residue calculations
2．3．Pieri formula and recurrence
2．3．1．Arms and legs again
2．3．2．Pieri formula
2．3．3．Recurrence
2．4．The Proof
2．4．1．The Schur case
2．4．2．Step one
2．4．3．Step two
2．4．4．Step three
References
编辑手记
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 聯絡我們
| 運費計算
| 幫助中心 |
加入書簽
HOME
新書上架
