Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70720
Title: | 於相應與表現 On correspondences and representations |
Authors: | He-Tong Shih 施和同 |
Advisor: | 莊武諺 |
Keyword: | 幾何表現,雙變論,卷積代數,相交上同調,卡司當-路斯提葛多項式,斯賓爵表現,希爾伯特點概形, geometric representations,bivariant theories,convolution algebra,intersection cohomology,Kazhdan-Lusztig polynomials,Springer representations,Hilbert schemes of points, |
Publication Year : | 2018 |
Degree: | 碩士 |
Abstract: | 本篇介紹簡單的幾何表現理論:描繪幾何,如舒伯特多樣體、史坦堡多樣體、希爾伯特點概形,與代數,如魏爾群、黑克代數、海森堡超代數,彼此間的關聯。將一代數結構以一幾何理論之相應操作或其卷積代數來表現,可視為代數與幾何間的橋樑,以分解原理為輔,並借助雙變論作為語言。其主要動機為希望透過抽象形式化來將這些現象統一詮釋。 This report introduces some simple geometric representation theories, describing relations between geometries such as Schubert varieties, Steinberg varieties, Hilbert schemes of points and algebras like Weyl groups, Hecke algebras, Heisenberg superalgebras. These bridges are representing an algebra by operations of correspondences of a geometric theory or its convolution algebra, with auxiliary of decomposition principle, via the language of bivariant theories. The main motivation is making an attempt to develop formalisms to unify interpretations of these phenomena. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70720 |
DOI: | 10.6342/NTU201801713 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
ntu-107-1.pdf Restricted Access | 743.44 kB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.