Ad-nilpotent ideals of complex and real reductive groups

In this thesis, we study ad-nilpotent ideals and its relations with nilpotent orbits, affine Weyl groups, sign types and hyperplane arrangements. This thesis is divided into three parts. The first and second parts deal with ad-nilpotent ideals for complex reductive Lie groups. In the first part, we study the left equivalence relation of ad-nilpotent ideals and relate it to some equivalence relation of affine Weyl groups and sign types. In the second part, we prove that for classical groups there always exist ideals of minimal dimension as conjectured by Sommers. In the third part, we define an analogous object for connected real reductive Lie groups, which is called 0-nilpotent subspaces. We relate 0-nilpotent subspaces to dominant regions of some real hyperplane arrangement and get the characteristic polynomials of the real hyperplane arrangement in the case of U(m, n) and Sp(m, n). We conjecture a general formula for other types.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Fang, Chuying

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/1721.1/41558

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/41558