Document Type

Dissertation

Date of Degree

Fall 2012

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Philip Kutzko

Abstract

Let A be a ring with involution *. The group Sl*(2,A), defined by Pantoja and Soto-Andrade, is a noncommutative version of Sl(2,F) where F is a field. In the case of A being artinian, they determined when Sl*(2,A) admitted a Bruhat presentation, and with Gutiérrez, constructed a representation for Sl*(2,A) from its generators. In particular, if A=Mn(F) and * is transposition, then Sl*(2,A) = Sp(2n,F). In this paper, we are interested in the representation theory of G=Sp4(O/p2) where A=M2(O/p2) and O is a local ring with prime ideal p. It has a normal, abelian subgroup K, and by Clifford's theorem we can find distinct irreducible representations of G starting with one-dimensional representations of K. The outline of our strategy will be demonstrated in the example of finding irreducible representations of SL2,(O/p2).

Keywords

representation theory

Pages

v, 40 pages

Bibliography

Includes bibliographical references (page 40).

Copyright

Copyright 2012 Carmen Wright

Included in

Mathematics Commons

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