2026-09-20T04:03:33Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/437352022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
David A. Vogan, Jr.
Gu, Jerin
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2008-12-11T16:55:57Z
2008-12-11T16:55:57Z
2008
2008
http://hdl.handle.net/1721.1/43735
261340987
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).
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).
by Jerin Gu.
Ph.D.
137 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Single-petaled K-types and Weyl group representations for classical groups
Thesis
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