The Derived Representation on the Lie Algebra
In this chapter for the first time we begin to deal with the C ∞ or (real) analytic structure of G, rather than with just measure theory. We shall see how a representation of G gives rise to an algebraic representation of the Lie algebra on a dense subspace, for an arbitrary Lie group G. In the case of SL 2(R), this representation has an especially simple form, as shown in §2.
KeywordsBanach Space Discrete Series Irreducible Unitary Representation High Weight Vector Algebraic Space
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