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dc.contributor.advisorDavid A. Vogan, Jr.en_US
dc.contributor.authorYee, Wai Ling, 1977-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2005-05-17T14:43:54Z
dc.date.available2005-05-17T14:43:54Z
dc.date.copyright2004en_US
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/16630
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.en_US
dc.descriptionIncludes bibliographical references (p. 79-80).en_US
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.description.abstractClassifying the irreducible unitary representations of a real reductive group is equivalent to the algebraic problem of classifying the Harish-Chandra modules admitting a positive definite invariant Hermitian form. Finding a formula for the signature of the Shapovalov form is a related problem which may be a necessary first step in such a classification. A Verma module may admit an invariant Hermitian form, which is unique up to multiplication by a real scalar when it exists. Suitably normalized, it is known as the Shapovalov form. The collection of highest weights decomposes under the affine Weyl group action into alcoves. The signature of the Shapovalov form for an irreducible Verma module depends only on the alcove in which the highest weight lies. We develop a formula for this signature, depending on the combinatorial structure of the affine Weyl group.en_US
dc.description.statementofresponsibilityby Wai Ling Yee.en_US
dc.format.extent80 p.en_US
dc.format.extent424571 bytes
dc.format.extent418741 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleOn the signature of the Shapovalov formen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc56019282en_US


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