Single-petaled K-types and Weyl group representations for classical groups

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).

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Gu, Jerin

Advisor dc:contributor.advisor

• David A. Vogan, Jr.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/43735

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/43735