Lie Groups pp 365-377 | Cite as

The Jacobi–Trudi Identity

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


For another account that derives the Jacobi-Trudi identity as a determinantal identity for characters of S n using Mackey theory see Kerber [100]. The point of view in Zelevinsky [178] is slightly different but also similar in spirit. We take up his Hopf algebra approach in the exercises. For us, the details were worked out some years ago in the Stanford senior thesis of Karl Rumelhart.


  1. 100.
    A. Kerber. Representations of permutation groups. I. Lecture Notes in Mathematics, Vol. 240. Springer-Verlag, Berlin, 1971.Google Scholar
  2. 124.
    I. Macdonald. Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995. With contributions by A. Zelevinsky, Oxford Science Publications.Google Scholar
  3. 125.
    S. Majid. A quantum groups primer, volume 292 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2002.Google Scholar
  4. 178.
    A. Zelevinsky. Representations of Finite Classical Groups, A Hopf algebra approach, volume 869 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1981.Google Scholar

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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