André, Carlos Alberto Martins (1992) Irreducible characters of the unitriangular group and coadjoint orbits. PhD thesis, University of Warwick.

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Abstract

The method of coadjoint orbits was introduced by Kirillov to study the unitary irreducible representations of a nilpotent Lie groups. Afterwards Kazhdan adapted this method to determine the irreducible complex characters of a finite unipotent group. We use this method to study the irreducible complex characters of any finite unitriangular group.

In chapters 2 and 5 we established an orthogonal decomposition of the regular character of any finite unitriangular group.

Chapters 3 and 4 are concerned with coadjoint orbits of any unitriangular group defined over an algebraically closed field. Chapter 3 is essentially the orbit version of chapter 2. In fact we obtain a decomposition of the dual space of the niltriangular Lie algebra as a disjoint union of invariant subvarieties. In a certain sense this decomposition corresponds to the one obtained in chapter 2 and 5.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Nilpotent Lie groups, Linear algebraic groups
Official Date:	May 1992
Dates:	Date Event May 1992 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Carter, Roger W. (Roger William)
Sponsors:	Fundação Calouste Gulbenkian
Format of File:	pdf
Extent:	xi, 248 leaves : illustrations
Language:	eng

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