Representations of sl2

  • William Fulton
  • Joe Harris
Part of the Graduate Texts in Mathematics book series (GTM, volume 129)


This is the first of four lectures—§11-14—that comprise in some sense the heart of the book. In particular, the naive analysis of §11.1, together with the analogous parts of §12 and §13, form the paradigm for the study of finite-dimensional representations of all semisimple Lie algebras and groups. §11.2 is less central; in it we show how the analysis carried out in §11.1 can be used to explicitly describe the tensor products of irreducible representations. §11.3 is least important; it indicates how we can interpret geometrically some of the results of the preceding section. The discussions in §11.1 and §11.2 are completely elementary (we do use the notion of symmetric powers of a vector space, but in a non-threatening way). §11.3 involves a fair amount of classical projective geometry, and can be skimmed or skipped by those not already familiar with the relevant basic notions from algebraic geometry.


Irreducible Representation Projective Space Symmetric Power Exterior Power Conic Curve 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • William Fulton
    • 1
  • Joe Harris
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

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