2026-09-19T22:34:24Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/601952022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Roman Bezrukavnikov.
Lin, Qian, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2010-12-06T17:36:29Z
2010-12-06T17:36:29Z
2010
2010
http://hdl.handle.net/1721.1/60195
681951804
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 45-47).
There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of a certain t-structure on the derived category of coherent sheaves on certain Springer Fiber. Meanwhile, a certain category of representation of Kac-Moody Lie algebra at critical level with (some) fixed central character is also equivalent to a core of certain t-structure on the same triangulated category. Based on several geometric results developed by Bezurkvanikov et al. these two abelian categories turn out to be equivalent. i.e. the two t-structures coincide.
Ph.D.
47 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Modules over affine lie algebras at critical level and quantum groups by Qian Lin.
Thesis
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Publication
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<Abstract>There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of a certain t-structure on the derived category of coherent sheaves on certain Springer Fiber. Meanwhile, a certain category of representation of Kac-Moody Lie algebra at critical level with (some) fixed central character is also equivalent to a core of certain t-structure on the same triangulated category. Based on several geometric results developed by Bezurkvanikov et al. these two abelian categories turn out to be equivalent. i.e. the two t-structures coincide.</Abstract>
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