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Lie Groups pp 71-79 | Cite as

Representations of \(\mathfrak{s}\mathfrak{l}(2, \mathbb{C})\)

  • Daniel Bump
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

Unless otherwise indicated, in this chapter a representation of a Lie group or Lie algebra is a complex representation. We remind the reader that if \(\mathfrak{g}\) is a complex Lie algebra [e.g. \(\mathfrak{s}\mathfrak{l}(2, \mathbb{C})\)], then a complex representation \(\pi: \mathfrak{g} \rightarrow \mathop{\rm End}\nolimits (V )\) is assumed to be complex linear, while if \(\mathfrak{g}\) is a real Lie algebra [e.g. \(\mathfrak{s}\mathfrak{u}(2)\) or \(\mathfrak{s}\mathfrak{l}(2, \mathbb{R})]\) then there is no such assumption.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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