Single-petaled K-types and Weyl group representations for classical groups
Name
261340987-MIT.pdf
Description
Full printable version
Size
501.44 KB
Format
Adobe PDF
Checksum (MD5)
995cdd7dfd36bd363c1301ac5dc50521
Author(s)
Gu, Jerin
Advisor(s)
David A. Vogan, Jr.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we show that single-petaled K-types and quasi-single-petaled K-types for reductive Lie groups generalize petite K-types for split groups. First, we prove that a Weyl group algebra element represents the action of the long intertwining operator for each single-petaled K-type, and then we demonstrate that a Weyl group algebra element represents a part of the long intertwining operator for each quasi-single-petaled K-type. We classify irreducible Weyl group representations realized by quasi-single-petaled K-types for classical groups. This work proves that every irreducible Weyl group representation is realized by quasi-single-petaled K-types for SL(n;C), SL(n;R), SU(m; n), SO(m; n), and Sp(n;R).
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 135-137).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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.
Persistent DSpace Link
