Representation theory of the finite unipotent linear groups
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. ^
"Representation theory of the finite unipotent linear groups"
(January 1, 2001).
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