SL2(R) pp 89-126 | Cite as

The Derived Representation on the Lie Algebra

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 105)


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.


Banach Space Discrete Series Irreducible Unitary Representation High Weight Vector Algebraic Space 
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Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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