2026-09-20T15:47:10Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/166302022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
David A. Vogan, Jr.
Yee, Wai Ling, 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-05-17T14:43:54Z
2005-05-17T14:43:54Z
2004
2004
http://hdl.handle.net/1721.1/16630
56019282
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 79-80).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Classifying 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.
by Wai Ling Yee.
Ph.D.
80 p.
424571 bytes
418741 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
On the signature of the Shapovalov form
Thesis
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