Representation theory of the finite unipotent linear groups / Ning Yan.

Format:

Book

Manuscript

Microformat

Thesis/Dissertation

Author/Creator:

Yan, Ning.

Contributor:

Kirillov, Alexandre A., advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

iv, 41 pages ; 29 cm

Production:

2001.

Summary:

The general linear group GLn,K over a field K contains a particularly prominent subgroup, the unipotent linear group ULn,K , consisting of all the unipotent upper triangular elements. In this paper we are interested in the case when K is the finite field Fq , and our goal is to better understand the representation theory of ULn,Fq . The complete classification of the complex irreducible representations of this group has long been known to be a difficult task. The traditional orbit method, famous for its success when K has characteristic 0, is a natural source of intuition and conjectures, but in our case the relation between coadjoint orbits and complex representations is still a mystery. Here we construct and study a subring in the representation ring of ULn,Fq , and build a theory with many of the major features one would expect from the philosophy of orbit method.

Notes:

Adviser: Alexandre A. Kirillov.

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2001.

Includes bibliographical references.

Local Notes:

University Microfilms order no.: 3015396.

OCLC:

244972481