對稱函式和麥克唐納多項式--余代數結構與Kawanaka恆等式

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.

圖書目錄

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

對稱函式和麥克唐納多項式--余代數結構與Kawanaka恆等式

基本介紹

內容簡介

圖書目錄

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