仿射根系統和麥當勞等式

Abstract

我們知道，在仿射根系統之下，麥當勞等式是一個Weyl等式的類似等式。本論文會分成兩個部分，第一部分會以介紹仿射根系統為主，提供定義和一些基本性質，最後則給出根系統的分類。而第二部份則會介紹麥當勞等式，以及給出三個特例，分別是當仿射根系統為A2, B2 and G2的形況。

It is knows that Macdonald’s identities are the analogues of the Weyl denominator formula for affine root system. The first part in this paper, we are going to introduce affine root systems and give some properties. Then, in the second part, we will discuss Macdonald’s identities and offer the cases when the types of affine root systems are A2, B2 and G2.