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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 于靖(Jing Yu) | |
| dc.contributor.author | Hung-You Chen | en |
| dc.contributor.author | 陳鴻猷 | zh_TW |
| dc.date.accessioned | 2021-05-11T05:06:30Z | - |
| dc.date.available | 2019-10-17 | |
| dc.date.available | 2021-05-11T05:06:30Z | - |
| dc.date.copyright | 2019-10-17 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-09-15 | |
| dc.identifier.citation | [D1] R. Dipper, G. James, Identification of the Irreducible Modular Representations of GLn(q), Journal of Algebra 104, 266-288, 1986.
[D2] R. Dipper, G. James, The q-Schur algebra, Proc. London Math. Soc. 59, 23-50, 1989. [F] W. Feit, The Representation Theory of Finite Groups, North Holland 1982. [FK] B. Ford, A. S. Kleshchev, A proof of the Mullineux conjecture, Math. Z. 226, 267-308, 1997. [FS] P. Fong and B. Srinivasan, The blocks of finite general linear and unitary groups, Inventiones Mathematicae 69, 109-154, 1982. [G] J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc. 80, 402-447, 1955. [GR] Darij Grinberg and Victor Reiner, Hopf algebras and combinatorics, 11 May 2018, arXiv:1409.8356v5 [H] Zhi-Hao Huang, On Characters of Symmetric Groups, Master Thesis, National Taiwan University, 2018. [J] G. D. James, The irreducible representations of the finite general linear groups, Proc. London Math. Soc. 52, 236-268, 1986. [J1] G. D. James, The Representation Theory of the Symmetric Groups, Springer 1978. [J2] G. D. James, Representations of General Linear Groups, London mathematical Society Lecture Notes 94, 1984 [J3] G. D. James, On the Decomposition Matrices of the Symmetric Groups II, JOURNAL OF ALGEBRA 43, 45-54, 1976. [K] A. S. Kleshchev, P. H. Tiep, Representations of finite special linear groups in non-defining characteristic, Advances in Mathematics 220, 478-504, 2009. [L] Yu-Chung Liu, On Lifting of Modular Characters, Master Thesis, National Taiwan University, 2017. [S] J. P. Serre, Linear Representations of Finite Groups, Springer GTM. [Sp1] T. Springer, Linear Algebraic Groups, Birkhauser, 2nd ed., 2009. [Sp2] T. Springer, Characters of special groups, in: Seminar on Algebraic Groups and Related Finite Groups, 121-166, Springer-Verlag, 1970. [web] http://www.math.rwth-aachen.de/˜MOC/decomposition/ | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/805 | - |
| dc.description.abstract | 本文討論置換群與有限一般線性群的分解矩陣的各種性質，分析不同性質之間的關係，並證明當特徵 p 不整除 q 時，有限特殊線性群亦擁有 (C, p)-性質。 | zh_TW |
| dc.description.abstract | In this thesis, we consider some properties of decomposition matrices of symmetric groups and finite general linear groups in non-defining characteristic, clarify the relations among these properties, and show that SL(n, q) has an analogue property to Sym(n) and GL(n, q) in non-defining characteristic, namely the (C, p)-property. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-11T05:06:30Z (GMT). No. of bitstreams: 1 ntu-108-R05221012-1.pdf: 1875482 bytes, checksum: bf4badd670ef20b57febc25b55e2e17b (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
致謝 ii 中文摘要 iii Abstract iv 0 Introduction 1 1 Preliminaries 6 1.1 Partitions 6 1.2 Group Theory 7 1.3 Conjugacy Classes in GLn(q) 9 1.4 Size of Conjugacy Classes of Rn 12 1.5 Representations and Modules 14 1.6 Characters 17 1.7 The Decomposition Matrix 20 1.8 Harish-Chandra Induction 21 2 Representation Theory of GLn(q) 22 2.1 Compositions, Tableaux and Permutations 22 2.2 Subgroups 24 2.3 Idempotents 26 2.4 The Module MF(s, (1)) 27 2.5 The Module MF(s, (1k)) 31 2.6 The Module MF(s, l), SF(s, l) and DF(s, l) 34 2.7 The Module SF(s, l) and DF(s, l) 39 3 Clifford Theory 42 3.1 Cyclic Quotient 43 3.2 Direct Product 45 3.3 Classification of Irreducible Representations of SLn 46 3.4 G-tile and S-tile 48 3.5 Representation Theory of G/S 51 4 Field Theory 53 4.1 Basic Facts 53 4.2 Elementary Number Theory 54 4.3 Degree Extension Lemma 56 4.4 Lemmas for Kleshchev-Tiep' s Theorem 59 5 Kleshchev-Tiep' s Theorem 62 6 Main Theorem 68 6.1 The Canonical Composition Factor 68 6.2 Main Results 71 6.3 Relations Between Branching Numbers 73 6.4 A Lower Unitriangular Submatrix 74 7 Conclusion 77 A Appendix 79 A.1 The Original Problem 79 A.2 The Implication Among Properties 82 A.3 The Decomposition Matrix of GL2 and SL2 84 A.4 The Decomposition Matrix of Other Groups 98 References 102 | |
| dc.language.iso | en | |
| dc.subject | 分解矩陣 | zh_TW |
| dc.subject | 有限一般線性群 | zh_TW |
| dc.subject | 群論 | zh_TW |
| dc.subject | 模表現論 | zh_TW |
| dc.subject | 有限特殊線性群 | zh_TW |
| dc.subject | modular representation | en |
| dc.subject | finite special linear group | en |
| dc.subject | group theory | en |
| dc.subject | decomposition matrix | en |
| dc.subject | finite general linear group | en |
| dc.title | 有限特殊線性群的特徵標 | zh_TW |
| dc.title | On characters of finite special linear groups in
non-defining characteristic | en |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 潘戍衍(Shu-Yen Pan),李華介(Hua-Chieh Li) | |
| dc.subject.keyword | 有限特殊線性群,模表現論,群論,分解矩陣,有限一般線性群, | zh_TW |
| dc.subject.keyword | finite special linear group,modular representation,group theory,decomposition matrix,finite general linear group, | en |
| dc.relation.page | 103 | |
| dc.identifier.doi | 10.6342/NTU201904116 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2019-09-16 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| ntu-108-1.pdf | 1.83 MB | Adobe PDF | View/Open |
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