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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 程舜仁(Shun-Jen Cheng) | |
| dc.contributor.author | Yu-Lun Cheng | en |
| dc.contributor.author | 鄭宇倫 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:23:07Z | - |
| dc.date.available | 2022-02-16 | |
| dc.date.available | 2022-11-23T09:23:07Z | - |
| dc.date.copyright | 2022-02-16 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-01-27 | |
| dc.identifier.citation | A. Beilinson and J. Bernstein. Localisation de g-modules. C. R. Acad. Sci. Paris Ser. I Math., 292(1):15–18, 1981. I. N. Bernstein, I. M. Gelfand, and S. I. Gelfand. Structure of representations that are generated by vectors of highest weight. Funckcional. Anal. i Prilozen., 5(1):1–9, 1971. I. N. Bernstein, I. M. Gelfand, and S. I. Gelfand. A certain category of g-modules. Funkcional. Anal. i Prilozen., 10(2):1–8, 1976. A. Beilinson, V. Ginzburg, and W. Soergel. Koszul duality patterns in representation theory. J. Amer. Math. Soc., 9(2):473–527, 1996. J.-L. Brylinski and M. Kashiwara. Kazhdan-Lusztig conjecture and holonomic systems. Invent. Math., 64(3):387–410, 1981. C.-W. Chen, S-.J. Cheng, and K. Coulembier. Tilting modules for classical Lie superalgebras. J. Lond. Math. Soc. (2), 103(3):870–900, 2021. C.-W. Chen, S.-J. Cheng, and L. Luo. Blocks and characters of G(3)-modules of non-integral weights. J. Algebra, 588:574–616, 2021. S.-J. Cheng and W. Wang. Dualities and Representations of Lie Superalgebras, volume 144 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2012. B. Elias, S. Makisumi, U. Thiel, and G. Williamson. Introduction to Soergel Bimodules, volume 5 of RSME Springer Series. Springer, Cham, 2020. M. Gorelik. Strongly typical representations of the basic classical Lie superalgebras. J. Amer. Math. Soc., 15(1):167–184, 2002. M. Geck and G. Pfeiffer. Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, volume 21 of London Mathematical Society Monographs. New Series. The Clarendon Press, Oxford University Press, New York, 2000. Harish-Chandra. On some applications of the universal enveloping algebra of a semisimple Lie algebra. Trans. Amer. Math. Soc., 70:28–96, 1951. James E. Humphreys. Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, Vol. 9. Springer-Verlag, New York-Berlin, 1972. J. E. Humphreys. Reflection Groups and Coxeter Groups, volume 29 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1990 J. E. Humphreys. Representations of Semisimple Lie Algebras in the BGG Category O, volume 94 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008. J. C. Jantzen. Moduln mit einem hochsten Gewicht, volume 750 of Lecture Notes in Mathematics. Springer, Berlin, 1979. V. Kac. Lie superalgebras. Adv. Math., 26(1):8–96, 1977. V. Kac. Representations of classical Lie superalgebras. In Differential geometrical methods in mathematical physics, II (Proc. Conf., Univ. Bonn, Bonn, 1977), volume 676 of Lecture Notes in Math., pages 597–626. Springer, Berlin, 1978. D. Kazhdan and G. Lusztig. Representations of Coxeter groups and Hecke algebras. Invent. Math., 53(2):165–184, 1979. D. Kazhdan and G. Lusztig. Schubert varieties and Poincare duality. In Geometry of the Laplace operator, Proc. Sympos. Pure Math., XXXVI, pages 185–203. American Mathematical Society, Providence, RI, 1980. G. Lusztig. Characters of Reductive Groups over a Finite Field, volume 107 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1984. I. M. Musson. Lie Superalgebras and Enveloping Algebras, volume 131 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2012. L. E. Ross. Representations of graded Lie algebras. Trans. Amer. Math. Soc.,120:17–23, 1965. W. Soergel. Kategorie O, perverse Garben und Moduln uber den Koinvarianten zur Weylgruppe. J. Amer. Math. Soc., 3(2):421–445, 1990. W. Soergel. Andersen filtration and hard Lefschetz. Geom. Funct. Anal., 17(6):2066–2089, 2008. D.-N. Verma. Structure of certain induced representations of complex semisimple Lie algebras. Bull. Amer. Math. Soc., 74:160–166, 1968. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80049 | - |
| dc.description.abstract | 在李超代數表現所形成的BGG範疇中，Gorelik證明了任意強典型區塊都與一個李代數表現的BGG範疇中的一個區塊等價。藉由將位移函子作用於合適的傾斜模並計算其結果的特徵標，我們證明了在李超代數B(m|1)的BGG範疇中，任意典型區塊都與一個強典型區塊等價，因此解決了李超代數B(m|1)在BGG範疇中的典型最高權不可約特徵標問題。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:23:07Z (GMT). No. of bitstreams: 1 U0001-2401202221413600.pdf: 292422 bytes, checksum: 67e57473373f47659a9e65e7c3312957 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Acknowledgements i Abstract ii 1 Introduction 1 2 Semisimple Lie algebras 3 2.1 Structure theory 3 2.2 Examples 6 2.3 Finite-dimensional representation 9 2.4 BGG category 13 3 Lie superalgebras 23 3.1 Basic definitions 23 3.2 Root systems of gl(m|n) and osp(2m+1|2n) 26 3.3 Representations 29 4 Main theorem 32 References 39 | |
| dc.language.iso | en | |
| dc.subject | BGG範疇 | zh_TW |
| dc.subject | 李代數 | zh_TW |
| dc.subject | 表現理論 | zh_TW |
| dc.subject | 不可約特徵標 | zh_TW |
| dc.subject | 李超代數 | zh_TW |
| dc.subject | representation theory | en |
| dc.subject | irreducible character | en |
| dc.subject | BGG category | en |
| dc.subject | Lie algebra | en |
| dc.subject | Lie superalgebra | en |
| dc.title | osp(2m+1|2)的典型最高權不可約特徵標 | zh_TW |
| dc.title | Irreducible characters of osp(2m+1|2) of typical highest weights | en |
| dc.date.schoolyear | 110-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.author-orcid | 0000-0002-1356-3393 | |
| dc.contributor.oralexamcommittee | 彭勇寧(Tien-Yi Chao),陳志瑋(Nai-Nu Yang),賴俊儒 | |
| dc.subject.keyword | 李代數,李超代數,表現理論,不可約特徵標,BGG範疇, | zh_TW |
| dc.subject.keyword | Lie algebra,Lie superalgebra,representation theory,irreducible character,BGG category, | en |
| dc.relation.page | 41 | |
| dc.identifier.doi | 10.6342/NTU202200190 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-01-29 | |
| 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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