GLn(C)的不可約表現建構方式之討論;On Some Constructions of Irreducible Representations of GLn(C)

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/96376

Title:	GLn(C)的不可約表現建構方式之討論;On Some Constructions of Irreducible Representations of GLn(C)
Authors:	宋狄謙;Sung, Di-Chian
Contributors:	數學系
Keywords:	不可約表現;Weyl模;最高權重;Irreducible representations;Weyl modules;Highest weight
Date:	2025-01-17
Issue Date:	2025-04-09 18:22:44 (UTC+8)
Publisher:	國立中央大學
Abstract:	在這篇文章中，我們討論兩種GLn(C)有限維的不可約表現之建構方式: Weyl 模和Highest weight定理。結果我們發現，Weyl模並不涵蓋所有GLn(C)的有限維不可約表現，比如說，對偶表現無法透過Weyl模來建構。因此，我們將透過其他的建構方式，來明確地刻劃出所有GLn(C)的有限維不可約表現。 ;There are two constructions of irreducible finite-dimensional representations of GLn(C): Weyl modules and Highest weight theory. It turns out that Weyl modules don’t give us all irreducible finite-dimensional representations of GLn(C). For example, dual representations are not included in Weyl modules. In this article, we explicitly describe all irreducible finite-dimensional representations of GLn(C) that don’t arise from Weyl modules.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	11	View/Open

社群 sharing