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Some representation theory of the group Sl*(2,A) where A=M(2,O/p^2) and * equals transpose

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 GutiƩrrez, 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).

Identiferoai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-3556
Date01 December 2012
CreatorsWright, Carmen
ContributorsKutzko, Philip C., 1946-
PublisherUniversity of Iowa
Source SetsUniversity of Iowa
LanguageEnglish
Detected LanguageEnglish
Typedissertation
Formatapplication/pdf
SourceTheses and Dissertations
RightsCopyright 2012 Carmen Wright

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