請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70720完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 莊武諺 | |
| dc.contributor.author | He-Tong Shih | en |
| dc.contributor.author | 施和同 | zh_TW |
| dc.date.accessioned | 2021-06-17T04:36:04Z | - |
| dc.date.available | 2018-09-14 | |
| dc.date.copyright | 2018-08-13 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-08-09 | |
| dc.identifier.citation | [1] Alexandre Beilinson and Joseph Bernstein. Localization of g-modules. COMPTES REN- DUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 292(1):15–18, 1981.
[2] IN Bernshtein, Izrail Moiseevich Gel’fand, and Sergei Izrail’evich Gel’fand. Structure of representations generated by vectors of highest weight. Functional analysis and its applications, 5(1):1–8, 1971. [3] Joseph Bernstein. Algebraic theory of D-modules. preprint, 1983. [4] Armand Borel. Intersection cohomology. Springer Science & Business Media, 2008. [5] Armand Borel, P-P Grivel, Burchard Kaup, and Andr ́e Haefliger. Algebraic D-modules. 1988. [6] Walter Borho and Macpherson. Representations des groupes de weyl et homologie d’intersection pour les variete nilpotents. CR Acad. Sci. Paris t., 292:707–710, 1981. [7] Jean-Luc Brylinski and Masaki Kashiwara. Kazhdan-lusztig conjecture and holonomic systems. Inventiones mathematicae, 64(3):387–410, 1981. [8] Neil Chriss and Victor Ginzburg. Representation theory and complex geometry. Springer Science & Business Media, 2009. [9] William Fulton and Robert MacPherson. Categorical framework for the study of singular spaces, volume 243. American Mathematical Soc., 1981. [10] V Ginsburg. g-modules, springer’s representations and bivariant chern classes. Advances in Mathematics, 61(1):1–48, 1986. [11] Victor Ginzburg. Geometrical aspects of representation theory. In Proceedings of the International Congress of Mathematicians, volume 1, page 2. Citeseer, 1986. [12] Victor Ginzburg. Geometric methods in the representation theory of hecke algebras and quantum groups. In Representation Theories and Algebraic Geometry, pages 127–183. Springer, 1998. [13] Mark Goresky and Robert MacPherson. Intersection homology theory. Topology, 19(2):135–162, 1980. [14] Mark Goresky and Robert MacPherson. Intersection homology II. Inventiones Mathe- maticae, 72(1):77–129, 1983. [15] Ryoshi Hotta, Kiyoshi Takeuchi, and Toshiyuki Tanisaki. D-modules, perverse sheaves, and representation theory, volume 236. Springer Science & Business Media, 2007. [16] Masaki Kashiwara. D-modules and representation theory of lie groups. In Annales de l’institut Fourier, volume 43, pages 1597–1618, 1993. [17] David Kazhdan and George Lusztig. Representations of coxeter groups and hecke alge- bras. Inventiones mathematicae, 53(2):165–184, 1979. [18] David Kazhdan and George Lusztig. Schubert varieties and poincar ́e duality. In Proc. Sympos. Pure Math, volume 36, pages 185–203, 1980. [19] Robert MacPherson. Global questions in the topology of singular spaces. In Proceedings of the International Congress of Mathematicians, volume 1, page 2, 1983. [20] Hiraku Nakajima. Lectures on Hilbert schemes of points on surfaces, volume 18. Amer- ican Mathematical Society Providence, RI, 1999. [21] Peter Slodowy. Simple singularities and simple algebraic groups, volume 815. Springer, 2006. [22] TA Springer. Quelques applications de la cohomologie d’intersection. S ́eminaire Bour- baki, 24:249–273, 1982. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70720 | - |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T04:36:04Z (GMT). No. of bitstreams: 1 ntu-107-R03221021-1.pdf: 761283 bytes, checksum: c493e9666697d951a0bfcbf386fd9ea8 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | Abstract 1
Introduction 4 1 Correspondence 6 1.1 Bivarianttheory.................................. 6 1.2 Correspondence.................................. 11 1.3 Borel-Moore homology .............................. 13 1.4 AlgebraicK-theory ................................ 15 1.5 Principle of decomposition............................ 17 1.6 Convolution algebra................................ 21 2 Some geometries 23 2.1 Schubert varieties................................. 23 2.2 Bott-Samelson desingularization......................... 25 2.3 Simultaneous resolution ............................. 26 2.4 Springer resolution ................................ 28 2.5 Hilbert schemes of points............................. 29 3 Some representations 30 3.1 Hecke algebra................................... 30 3.2 Weyl group .................................... 34 3.3 Heisenberg superalgebra ............................. 36 Bibliography 38 | |
| dc.language.iso | en | |
| dc.subject | 雙變論 | zh_TW |
| dc.subject | 卡司當－路斯提葛多項式 | zh_TW |
| dc.subject | 幾何表現 | zh_TW |
| dc.subject | 斯賓爵表現 | zh_TW |
| dc.subject | 希爾伯特點概形 | zh_TW |
| dc.subject | 相交上同調 | zh_TW |
| dc.subject | 卷積代數 | zh_TW |
| dc.subject | bivariant theories | en |
| dc.subject | Kazhdan-Lusztig polynomials | en |
| dc.subject | Springer representations | en |
| dc.subject | Hilbert schemes of points | en |
| dc.subject | geometric representations | en |
| dc.subject | convolution algebra | en |
| dc.subject | intersection cohomology | en |
| dc.title | 於相應與表現 | zh_TW |
| dc.title | On correspondences and representations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳榮凱,崔茂培 | |
| dc.subject.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, | zh_TW |
| dc.subject.keyword | geometric representations,bivariant theories,convolution algebra,intersection cohomology,Kazhdan-Lusztig polynomials,Springer representations,Hilbert schemes of points, | en |
| dc.relation.page | 39 | |
| dc.identifier.doi | 10.6342/NTU201801713 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-08-09 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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