Abstract/Details

Generating equivalence classes of B -stable ideals


2008 2008

Other formats: Order a copy

Abstract (summary)

This thesis deals with structures found in semisimple Lie algebras called B-stable ideals. We develop a series of simple "moves", ways to move from one B-stable ideal to a smaller one, that preserve certain data arising from each ideal. Specifically, each ideal corresponds to a nilpotent orbit in the Lie algebra and we present a set of moves allowing us to create equivalence classes of ideals corresponding to the same orbit. Additionally, each ideal corresponds to a subgroup of the component group associated to its orbit and we similarly use a set of moves to look at equivalence classes of ideals corresponding to conjugate subgroups. Finally, we analyze these equivalence classes in light of some previously known geometric results, leading us to information about the Springer fiber associated to a given orbit.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, B-stable ideals, Equivalence classes, Nilpotent orbits, Semisimple Lie algebras
Title
Generating equivalence classes of B -stable ideals
Author
Fenn, Molly
Number of pages
92
Publication year
2008
Degree date
2008
School code
0118
Source
DAI-B 69/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549789246
Advisor
Sommers, Eric
Committee member
Braden, Tom; Mirkovic, Ivan; Moll, Robert
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3325248
ProQuest document ID
304574139
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304574139
Access the complete full text

You can get the full text of this document if it is part of your institution's ProQuest subscription.

Try one of the following:

  • Connect to ProQuest through your library network and search for the document from there.
  • Request the document from your library.
  • Go to the ProQuest login page and enter a ProQuest or My Research username / password.