Single-petaled K-types and Weyl group representations for classical groups
Author(s)
Gu, Jerin
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
David A. Vogan, Jr.
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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).
Date issued
2008Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.