On the signature of the Shapovalov form
Name
56019282-MIT.pdf
Description
Full printable version
Size
408.93 KB
Format
Adobe PDF
Checksum (MD5)
26dea922f55fdfcaa58c477523902f6b
Author(s)
Yee, Wai Ling, 1977-
Advisor(s)
David A. Vogan, Jr.
Date Issued
2004
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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.
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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