well developed case ''g'' locally compact hausdorff topological group representations strongly continuous ref name folland ''g'' abelian unitary dual space characters ''g'' compact peter weyl theorem shows irreducible unitary representations finite dimensional unitary dual discrete ref name peter weyl ref example ''g'' circle group ''s'' sup sup characters given integers unitary dual '''z''' non compact ''g'' question representations unitary subtle one although irreducible unitary representations must admissible
Formal science Mathematics Pure mathematics Algebra Representation theory