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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 于靖(Jing Yu) | |
dc.contributor.author | Zih-Hao Huang | en |
dc.contributor.author | 黃子豪 | zh_TW |
dc.date.accessioned | 2021-05-12T09:34:44Z | - |
dc.date.available | 2018-05-31 | |
dc.date.available | 2021-05-12T09:34:44Z | - |
dc.date.copyright | 2018-05-31 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-05-23 | |
dc.identifier.citation | References
[B] D. Benson, Spin Modules for Symmetric Groups, Journal of the London Mathematical Society, s2-38(2), 250-262, 1988. [CR] C. Curtis and I. Reiner, Methods of Representation Theory I, II. Wiley-Interscience 1981. [F] W. Fulton and J. Harris, Representation Theory: A First Course, Springer GTM. [F1] M. Fayers, On the Irreducible Representation of the Alternating Group which Remain Irreducible in Characteristic $p$, Representation Theory Amer. Math. Soc., 14, 601-626, 2010. [F2] M. Fayers, The Irreducible Representations of the Alternating group which Remain Irreducible in Characteristic $p$, Transactions Amer. Math. Soc., 368(8), 5807–5855, 2016. [I] I. M. Isaacs, Character Theory of Finite Groups, Academic Press. [J1] G. D. James, The Representation Theory of the Symmetric Groups, Springer 1978. [J2] G. D. James, On the Decomposition Matrices of the Symmetric Groups. II, Journal of Algebra, 43(13), 45-54, 1976. [L] Yu-Chung Liu, On Lifting of Modular Characters, Master's Thesis of Department of Mathematics, National Taiwan University, Taipei, 2017. [R] G. de B. Robinson, Representation Theory of the Symmetric Group, Edinburgh University Press, 1961. [S1] J. P. Serre, Linear Representations of Finite Groups, Springer GTM. [S2] J. P. Serre, Local Fields, Springer GTM. [W] M. Wildon, Character Values and Decomposition Matrices of Symmetric Groups, Journal of Algebra, 319(8), 3382-3397, 2008. [web] http://www.math.rwth-aachen.de/homes/MOC/decomposition/tex/ON/ON.2mod2.pdf [web2] http://www.math.rwth-aachen.de/homes/MOC/decomposition/ | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1241 | - |
dc.description.abstract | 令 p 為一個質數,G 為一個有限群,且 G^(p) 為收集 G 的元素中所有滿足元素的階 (order) 和 p 互質的元素。如果對於所有的 G 的不可約特徵標 (irreducible character) X,都沒辦法找到一個大於 1 的自然數 a 和一個 G 的不可約 p-模特徵標 φ (irreducible p-modular character)使得 X|_{G^(p)} = aφ,那我們就會說G有 (L ', p)-性質 ((L ', p)-property)。如果對於所有的 G 的不可約特徵標 X,都能找到一個 G 的不可約 p-模特徵標 φ 使得 X|_{G^(p)} ≥ φ with multiplicity 1,那我們就會說 G 有 (L ' ', p)-性質 ((L ' ', p)-property)。又如果對於所有的質數 p,G 恆有 (L ' ', p)-性質,那我們就會說 G有 L ' '-性質 (L ' '-property)。
在這篇碩士論文中,我們想要證明所有的對稱群 (symmetric groups) 都有 L ' '-性質;所有的交錯群 (alternating groups) 都有 (L ' ',2)-性質;且對於所有比 2 大的質數 p,所有的交錯群都有 (L ', p)-性質。 | zh_TW |
dc.description.abstract | Let p be a prime number, G be a finite group,and G^(p) be the set of all g ∈ G such that p ∤ ord(g). We say G has the (L ', p)-property if for any irreducible character X of G, X|_{G^(p)} ≠ aφ for any irreducible p-modular character φ of G and any a∈N with a > 1. We say G has the (L ' ', p)-property if for any irreducible character X of G, there exists an irreducible p-modular character φ of G such that X|_{G^(p)} ≥ φ with multiplicity 1. We say
G has the L ' '-property if G has the (L ' ', p)-property for all p. In this thesis, we want to show that all symmetric groups have the L ' '-property, all alternating groups have the (L ' ',2)-property, and all alternating groups have the (L ', p)-property for all prime p > 2. | en |
dc.description.provenance | Made available in DSpace on 2021-05-12T09:34:44Z (GMT). No. of bitstreams: 1 ntu-107-R04221002-1.pdf: 3159178 bytes, checksum: de5d694bf029ff4d2b210bcc62bf5902 (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | Contents
口試委員會審定書 i 致謝 ii 中文摘要 iii Abstract iv 0 Notations and Preliminaries 1 1 Introduction 7 2 Specht modules, F0Sn-Modules, and FpSn-modules 11 2.1 The Definition of the Specht Module 11 2.2 Simple F0Sn-Module and Simple FpSn-Module 14 2.3 Facts about F0Sn-Module and FpSn-Module 19 3 About Sn 22 3.1 Groups S5 and S6 have the (L ', p)-property 22 3.2 Diagrams 32 3.3 The L ' '-Property of Sn 43 4 About An 56 4.1 Tools 57 4.2 The (L ' ',2)-property of An 65 4.3 The (L ', p)-property of An for p > 2 67 5 Appendix A: Letter from Jean-Pierre Serre 79 6 Appendix B: Proof of Serre’s Exercise in Appendix A 81 Reference 87 | |
dc.language.iso | en | |
dc.title | 在對稱群上的特徵標 | zh_TW |
dc.title | On Characters of Symmetric Groups | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 李華介,林惠雯,潘戍衍 | |
dc.subject.keyword | 對稱群,交錯群,特徵標,p-模特徵標,(L ,p)-性質,L -性質, | zh_TW |
dc.subject.keyword | symmetric groups,alternating groups,character,modular character,(L ,p)-property,L -property, | en |
dc.relation.page | 88 | |
dc.identifier.doi | 10.6342/NTU201800842 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2018-05-23 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
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