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Nilpotent orbits in bad characteristic and the Springer correspondence

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dc.contributor.advisor George Lusztig. en_US
dc.contributor.author Xue, Ting, Ph. D. Massachusetts Institute of Technology en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.date.accessioned 2010-12-06T17:37:26Z
dc.date.available 2010-12-06T17:37:26Z
dc.date.copyright 2010 en_US
dc.date.issued 2010 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/60202
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 109-112). en_US
dc.description.abstract Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p, g the Lie algebra of G and g* the dual vector space of g. This thesis is concerned with nilpotent orbits in g and g* and the Springer correspondence for g and g* when p is a bad prime. Denote W the set of isomorphism classes of irreducible representations of the Weyl group W of G. Fix a prime number 1 7 p. We denote ... the set of all pairs (c, F), where c is a nilpotent G-orbit in g (resp. g*) and F is an irreducible G-equivariant Q1-local system on c (up to isomorphism). In chapter 1, we study the Springer correspondence for g when G is of type B, C or D (p = 2). The correspondence is a bijective map from W to 2t.. In particular, we classify nilpotent G-orbits in g (type B, D) over finite fields of characteristic 2. In chapter 2, we study the Springer correspondence for g* when G is of type B, C or D (p = 2). The correspondence is a bijective map from ... . In particular, we classify nilpotent G-orbits in g* over algebraically closed and finite fields of characteristic 2. In chapter 3, we give a combinatorial description of the Springer correspondence constructed in chapter 1 and chapter 2 for 8 and g*. In chapter 4, we study the nilpotent orbits in 8* and the Weyl group representations that correspond to the pairs ... under Springer correspondence when G is of an exceptional type. Chapters 1, 2 and 3 are based on the papers [X1, X2, X3]. Chapter 4 is based on some unpublished work. en_US
dc.description.statementofresponsibility by Ting Xue. en_US
dc.format.extent 112 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Mathematics. en_US
dc.title Nilpotent orbits in bad characteristic and the Springer correspondence en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 681968408 en_US


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