Pitt Logo LinkContact Us

Nilpoten Conjugacy Classes of Reductive p-adic Lie Algebras and Definability in Pas's Language

Diwadkar, Jyotsna Mainkar (2006) Nilpoten Conjugacy Classes of Reductive p-adic Lie Algebras and Definability in Pas's Language. Doctoral Dissertation, University of Pittsburgh.

[img]
Preview
PDF - Primary Text
Download (561Kb) | Preview

    Abstract

    We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over p-adic fields definable by a formula in Pas's language. We answer in the affirmative in three cases: special orthogonal Lie algebras so(n) for n odd, special linear Lie algebra sl(3) and the exceptional Lie algebra G2 over p-adic fields. The nilpotent conjugacy classes in these three cases have been parameterized by Waldspurger (so(n)) and S. DeBacker(sl(3), G2). For sl (3) and G2 we are required to extend Pas's language by a finite number of symbols.


    Share

    Citation/Export:
    Social Networking:

    Details

    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairHales, Thomas Chales@pitt.edu
    Committee MemberConstantine, Gregory Mgmc@pitt.edu
    Committee MemberFulman, Jasonfulman@usc.edu
    Committee MemberAvigad, Jeremyavigad@andrew.cmu.edu
    Title: Nilpoten Conjugacy Classes of Reductive p-adic Lie Algebras and Definability in Pas's Language
    Status: Unpublished
    Abstract: We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over p-adic fields definable by a formula in Pas's language. We answer in the affirmative in three cases: special orthogonal Lie algebras so(n) for n odd, special linear Lie algebra sl(3) and the exceptional Lie algebra G2 over p-adic fields. The nilpotent conjugacy classes in these three cases have been parameterized by Waldspurger (so(n)) and S. DeBacker(sl(3), G2). For sl (3) and G2 we are required to extend Pas's language by a finite number of symbols.
    Date: 20 September 2006
    Date Type: Completion
    Defense Date: 11 July 2006
    Approval Date: 20 September 2006
    Submission Date: 01 August 2006
    Access Restriction: No restriction; The work is available for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-08012006-134916
    Uncontrolled Keywords: affine apartments; special orhtogonal
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:55
    Last Modified: 06 Jun 2012 15:01
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-08012006-134916/, etd-08012006-134916

    Actions (login required)

    View Item

    Document Downloads